Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter...
Transcript of Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter...
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Section 2.1
Increasing, Decreasing, and Piecewise Functions; Appli-cations
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Features ofGraphs
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Intervals of Increase and Decrease
A function is increasing when the graph goes up as you travel along itfrom left to right.
A function is decreasing when the graph goes down as you travel along itfrom left to right.A function is constant when the graph is a perfectly flat horizontal line.For example:
When we describe where the function is increasing, decreasing, andconstant, we write open intervals written in terms of the x-values wherethe function is increasing or decreasing.
![Page 4: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/4.jpg)
Intervals of Increase and Decrease
A function is increasing when the graph goes up as you travel along itfrom left to right.A function is decreasing when the graph goes down as you travel along itfrom left to right.
A function is constant when the graph is a perfectly flat horizontal line.For example:
When we describe where the function is increasing, decreasing, andconstant, we write open intervals written in terms of the x-values wherethe function is increasing or decreasing.
![Page 5: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/5.jpg)
Intervals of Increase and Decrease
A function is increasing when the graph goes up as you travel along itfrom left to right.A function is decreasing when the graph goes down as you travel along itfrom left to right.A function is constant when the graph is a perfectly flat horizontal line.
For example:
When we describe where the function is increasing, decreasing, andconstant, we write open intervals written in terms of the x-values wherethe function is increasing or decreasing.
![Page 6: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/6.jpg)
Intervals of Increase and Decrease
A function is increasing when the graph goes up as you travel along itfrom left to right.A function is decreasing when the graph goes down as you travel along itfrom left to right.A function is constant when the graph is a perfectly flat horizontal line.For example:
When we describe where the function is increasing, decreasing, andconstant, we write open intervals written in terms of the x-values wherethe function is increasing or decreasing.
![Page 7: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/7.jpg)
Intervals of Increase and Decrease
A function is increasing when the graph goes up as you travel along itfrom left to right.A function is decreasing when the graph goes down as you travel along itfrom left to right.A function is constant when the graph is a perfectly flat horizontal line.For example:
decreasing
incr
easi
ng
constant
decreasin
g
incr
easi
ng
decreasing
When we describe where the function is increasing, decreasing, andconstant, we write open intervals written in terms of the x-values wherethe function is increasing or decreasing.
![Page 8: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/8.jpg)
Relative Maximums and Minimums
Relative maximums (more properly maxima) are points that arehigher than all nearby points on the graph.
Relative minimums (more properly minima) are points that arelower than all nearby points on the graph.The phrase relative extrema refers to both relative maximums andminimums.For example:
![Page 9: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/9.jpg)
Relative Maximums and Minimums
Relative maximums (more properly maxima) are points that arehigher than all nearby points on the graph.Relative minimums (more properly minima) are points that arelower than all nearby points on the graph.
The phrase relative extrema refers to both relative maximums andminimums.For example:
![Page 10: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/10.jpg)
Relative Maximums and Minimums
Relative maximums (more properly maxima) are points that arehigher than all nearby points on the graph.Relative minimums (more properly minima) are points that arelower than all nearby points on the graph.The phrase relative extrema refers to both relative maximums andminimums.
For example:
![Page 11: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/11.jpg)
Relative Maximums and Minimums
Relative maximums (more properly maxima) are points that arehigher than all nearby points on the graph.Relative minimums (more properly minima) are points that arelower than all nearby points on the graph.The phrase relative extrema refers to both relative maximums andminimums.For example:
Relative Minimum
Relative Minimum
Relative Maximum
![Page 12: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/12.jpg)
Examples
1. The graph of g(x) is given. Find all relative maximums andminimums as well as the intervals of increase and decrease.
−12−10 −8 −6 −4 −2 2 4 6
−6
−4
−2
2
4
6
8
10
Relative Maximums:8 at x = −6.Relative Minimums:-2 at x = 2.Intervals of Increase:(−∞,−6) ∪ (2,∞)Intervals of Decrease:
(−6, 2)
![Page 13: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/13.jpg)
Examples
1. The graph of g(x) is given. Find all relative maximums andminimums as well as the intervals of increase and decrease.
−12−10 −8 −6 −4 −2 2 4 6
−6
−4
−2
2
4
6
8
10Relative Maximums:8 at x = −6.Relative Minimums:-2 at x = 2.Intervals of Increase:(−∞,−6) ∪ (2,∞)Intervals of Decrease:
(−6, 2)
![Page 14: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/14.jpg)
Examples (continued)
2. The graph of h(x) is given. Find the intervals where h(x) isincreasing, decreasing and constant. Then find the domain andrange.
−12 −10 −8 −6 −4 −2 2 4
−4
−3
−2
−1
1
2
3
4
Increasing: (−∞,−8) ∪ (−3,−1)Decreasing: (−8,−6)Constant: (−6,−3) ∪ (−1,∞)Domain:(−∞,∞)
Range:(−∞, 4]
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Examples (continued)
2. The graph of h(x) is given. Find the intervals where h(x) isincreasing, decreasing and constant. Then find the domain andrange.
−12 −10 −8 −6 −4 −2 2 4
−4
−3
−2
−1
1
2
3
4
Increasing: (−∞,−8) ∪ (−3,−1)Decreasing: (−8,−6)Constant: (−6,−3) ∪ (−1,∞)Domain:(−∞,∞)
Range:(−∞, 4]
![Page 16: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/16.jpg)
Applications
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Example
Creative Landscaping has 60 yd of fencing with which to enclose arectangular flower garden. If the garden is x yards long, express thegarden’s area as a function of its length. Use a graphing device todetermine the maximum area of the garden.
A(x) = x(30− x)Maximum Area: 225 square yards
![Page 18: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/18.jpg)
Example
Creative Landscaping has 60 yd of fencing with which to enclose arectangular flower garden. If the garden is x yards long, express thegarden’s area as a function of its length. Use a graphing device todetermine the maximum area of the garden.
A(x) = x(30− x)Maximum Area: 225 square yards
![Page 19: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/19.jpg)
Piecewise Functions
![Page 20: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/20.jpg)
Definition
A piecewise function has several formulas to compute the output. Theformula used depends on the input value.For example,
|x | =
{x if x ≥ 0−x if x < 0
![Page 21: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/21.jpg)
Examples
If h(t) =
0 if t < −212tt−1 if − 2 ≤ t < 1
4t − 3 if t ≥ 1
, find
1. h(0)
0
2. h
(4
3
)7
3
3. h(−100)
0
![Page 22: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/22.jpg)
Examples
If h(t) =
0 if t < −212tt−1 if − 2 ≤ t < 1
4t − 3 if t ≥ 1
, find
1. h(0)
0
2. h
(4
3
)7
3
3. h(−100)
0
![Page 23: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/23.jpg)
Examples
If h(t) =
0 if t < −212tt−1 if − 2 ≤ t < 1
4t − 3 if t ≥ 1
, find
1. h(0)
0
2. h
(4
3
)
7
3
3. h(−100)
0
![Page 24: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/24.jpg)
Examples
If h(t) =
0 if t < −212tt−1 if − 2 ≤ t < 1
4t − 3 if t ≥ 1
, find
1. h(0)
0
2. h
(4
3
)7
3
3. h(−100)
0
![Page 25: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/25.jpg)
Examples
If h(t) =
0 if t < −212tt−1 if − 2 ≤ t < 1
4t − 3 if t ≥ 1
, find
1. h(0)
0
2. h
(4
3
)7
3
3. h(−100)
0
![Page 26: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/26.jpg)
Examples
If h(t) =
0 if t < −212tt−1 if − 2 ≤ t < 1
4t − 3 if t ≥ 1
, find
1. h(0)
0
2. h
(4
3
)7
3
3. h(−100)
0
![Page 27: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/27.jpg)
Graphing
1. Split apart the function into the separate formulas. Determine whatthe graphs of each of those formulas looks like separately.
2. Use the inequalities to figure out what “section” you need from eachgraph.
3. Put all the “sections” together on a single graph, making sure tocorrectly plot the endpoints.
< or > - use an open circle≤ or ≥ - use a closed circle
None of the sections should have any vertical overlap! (Otherwise, itfails the vertical line test so what you’ve drawn isn’t a function.)
![Page 28: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/28.jpg)
Graphing
1. Split apart the function into the separate formulas. Determine whatthe graphs of each of those formulas looks like separately.
2. Use the inequalities to figure out what “section” you need from eachgraph.
3. Put all the “sections” together on a single graph, making sure tocorrectly plot the endpoints.
< or > - use an open circle≤ or ≥ - use a closed circle
None of the sections should have any vertical overlap! (Otherwise, itfails the vertical line test so what you’ve drawn isn’t a function.)
![Page 29: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/29.jpg)
Graphing
1. Split apart the function into the separate formulas. Determine whatthe graphs of each of those formulas looks like separately.
2. Use the inequalities to figure out what “section” you need from eachgraph.
3. Put all the “sections” together on a single graph, making sure tocorrectly plot the endpoints.
< or > - use an open circle≤ or ≥ - use a closed circle
None of the sections should have any vertical overlap! (Otherwise, itfails the vertical line test so what you’ve drawn isn’t a function.)
![Page 30: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/30.jpg)
Graphing
1. Split apart the function into the separate formulas. Determine whatthe graphs of each of those formulas looks like separately.
2. Use the inequalities to figure out what “section” you need from eachgraph.
3. Put all the “sections” together on a single graph, making sure tocorrectly plot the endpoints.
< or > - use an open circle
≤ or ≥ - use a closed circle
None of the sections should have any vertical overlap! (Otherwise, itfails the vertical line test so what you’ve drawn isn’t a function.)
![Page 31: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/31.jpg)
Graphing
1. Split apart the function into the separate formulas. Determine whatthe graphs of each of those formulas looks like separately.
2. Use the inequalities to figure out what “section” you need from eachgraph.
3. Put all the “sections” together on a single graph, making sure tocorrectly plot the endpoints.
< or > - use an open circle≤ or ≥ - use a closed circle
None of the sections should have any vertical overlap! (Otherwise, itfails the vertical line test so what you’ve drawn isn’t a function.)
![Page 32: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/32.jpg)
Graphing
1. Split apart the function into the separate formulas. Determine whatthe graphs of each of those formulas looks like separately.
2. Use the inequalities to figure out what “section” you need from eachgraph.
3. Put all the “sections” together on a single graph, making sure tocorrectly plot the endpoints.
< or > - use an open circle≤ or ≥ - use a closed circle
None of the sections should have any vertical overlap! (Otherwise, itfails the vertical line test so what you’ve drawn isn’t a function.)
![Page 33: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/33.jpg)
Examples
1. Graph
f (x) =
−x if x ≤ 0
4− x2 if 0 < x ≤ 3x − 3 if x > 3
−4−3−2−1 1 2 3 4
−5
−4
−3
−2
−1
1
2
3
4
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Examples
1. Graph
f (x) =
−x if x ≤ 0
4− x2 if 0 < x ≤ 3x − 3 if x > 3
−4−3−2−1 1 2 3 4
−5
−4
−3
−2
−1
1
2
3
4
![Page 35: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/35.jpg)
Examples (continued)
2. Graph
f (x) =
0 if x ≤ 1
(x − 1)2 if 1 < x < 3−x + 1 if x ≥ 3
−4−3−2−1 1 2 3 4
−4
−3
−2
−1
1
2
3
4
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Examples (continued)
2. Graph
f (x) =
0 if x ≤ 1
(x − 1)2 if 1 < x < 3−x + 1 if x ≥ 3
−4−3−2−1 1 2 3 4
−4
−3
−2
−1
1
2
3
4
![Page 37: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/37.jpg)
Greatest Integer Function
The greatest integer function, y = JxK, rounds every number down to thenearest integer.
−4 −3 −2 −1 1 2 3 4
−4
−3
−2
−1
1
2
3
4
JxK =
...−2 if −2 ≤ x < −1−1 if −1 ≤ x < 0
0 if 0 ≤ x < 11 if 1 ≤ x < 22 if 2 ≤ x < 3...
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Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3
![Page 39: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/39.jpg)
Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3
![Page 40: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/40.jpg)
Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3
![Page 41: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/41.jpg)
Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3
![Page 42: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/42.jpg)
Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3
![Page 43: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/43.jpg)
Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3
![Page 44: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/44.jpg)
Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3
![Page 45: Section 2.1 - Increasing, Decreasing, and Piecewise ...ain.faculty.unlv.edu/124 Notes/Chapter 2/Section 2.1 Presentation.pdf · Graphing 1.Split apart the function into the separate](https://reader033.fdocuments.net/reader033/viewer/2022050102/5f40e9683172bc18bc43c927/html5/thumbnails/45.jpg)
Examples
1. J−22.5K
−23
2. J4.7K
4
3. J30K
30
4. Find the range of values that x couldbe.
JxK2 = 16
4 ≤ x < 5 or −4 ≤ x < −3