Do Now: Write the recursive formula for the following problems or write the pattern. 1.a 1 = -3, a n...
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Transcript of Do Now: Write the recursive formula for the following problems or write the pattern. 1.a 1 = -3, a n...
Do Now:
Write the recursive formula for the following problems or write the pattern. 1.a1= -3, an = an-1 +3
2. a1= -2, an = 2an-1
3.256, 64, 16, 4, 1 …4. 3, 7, 11, 15, 19
Objective:
• To graph square root functions.
Vocab.
• A radical expression is an expression that contains a radical sign.
• If the radical is a square root then it’s called a square root function.
Parent Square Root Function:
EXAMPLE 1
SOLUTION
STEP 1
Graph a function of the form y = a x
Graph the function y = 3 x and identify its domain and range. Compare the graph with the graph of y = x .
Make a table. Because the square root of a negative number is undefined, x must be nonnegative. So, the domain is x ≥ 0.
STEP 2
Plot the points.
EXAMPLE 1
STEP 3
Graph a function of the form y = a x
STEP 4
Draw a smooth curve through the points. From either the table or the graph, you can see the range of the function is y ≥ 0.
Compare the graph with the graph of y = x . The graph of y = 3 x is a vertical stretch (by a factor of 3) of the graph of y = x .
EXAMPLE 2 Graph a function of the form y = a x
SOLUTION
Graph the function y = –0.5 x and identify its domain and range. Compare the graph with the graph of y = x .
To graph the function, make a table, plot the points, and draw a smooth curve through the points. The domain is x ≥ 0.
The range is y ≤ 0.The graph of y = –0.5 x is a vertical shrink (by a factor of 0.5) with a reflection in the x-axis of the graph of y = x .
EXAMPLE 3 Graph a function of the form y = x + k
SOLUTION
Graph the function y = x + 2 and identify its domain and range. Compare the graph with the graph of y = x .
To graph the function, make a table, then plot and connect the points. The domain is x ≥ 0.
The range is y ≥ 2.The graph of y = x + 2 is a vertical translation (of 2 units up) of the graph of y = x .
GUIDED PRACTICE for Examples 1, 2 and 3
Graph the function and identify its domain and range. Compare the graph with the graph of y = x .
1. y = 2 x
ANSWER
Domain: x ≥ 0, Range: y ≥ 0Vertical stretch by a factor of 2
GUIDED PRACTICE for Examples 1, 2 and 3
Graph the function and identify its domain and range. Compare the graph with the graph of y = x .
2. y = x – 1
Domain: x ≥ 0, Range: y ≥ 0 – 1Vertical translation of 1 unit down
ANSWER
GUIDED PRACTICE for Examples 1, 2 and 3
Graph the function and identify its domain and range. Compare the graph with the graph of y = x .
3. y = x + 3
Domain: x ≥ 0, Range: y ≤ 0Vertical translation of 3 units up
ANSWER
EXAMPLE 4
SOLUTION
Graph a function of the form y = x – h
Graph the function y = x – 4 and identify its domain and range. Compare the graph with the graph of y = x .
To graph the function, make a table, then plot and connect the points. To find the domain, find the values of x for which the radicand, x – 4 , is nonnegative. The domain is x ≥ 4.
EXAMPLE 4 Graph a function of the form y = x – h
The range is y ≥ 0.The graph of y = x – 4 is a horizontal translation (of 4 units to the right) of the graph of y = .x
EXAMPLE 5 Graph a function of the form y = a x – h + k
x + 4Graph the function y = 2 – 1 .
SOLUTION
STEP 1
Sketch the graph of y = 2 .x
STEP 2
So, h = –4 and k = –1. Shift the graph left 4 units and down 1 unit.
y = 2 – 1 = 2 x – (–4) + (–1). x + 4
Shift the graph h units horizontally and k units vertically. Notice that
Exit Ticket for Examples 4 and 5
Graph the function y = x + 3 and identify its domain and range. Compare the graph with the graph of y = x .
Domain: x ≥ – 3; Range: y ≥ 0; Horizontal translation 3 units to the left
ANSWER
GUIDED PRACTICE for Examples 4 and 5
6. Identify the domain and range of the function in Example 5.
The domain is x ≥ – 4. The range is y ≥ –1.
ANSWER