Post on 31-Dec-2015
04/19/23 22:04 8-7: Square Root Graphs 1
SQUARE ROOT SQUARE ROOT Functions Functions
Radical functionsRadical functions
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REVIEWREVIEWA radical function is a function whose rule is a radical expression, which include the square-root function, x
f x x
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EXAMPLE 1EXAMPLE 1Graph each function and identify its domain and range of 2 1f x x
1x 0y Domain: Range:
g(x)x f(x) 2 1f x x
0246
2 1 1 2 0 12 0 1 2 1
2 3 1 2 2
2 8 1 2 3
0
38
1x x 0y y
0, 1,
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EXAMPLE 2EXAMPLE 2Graph each function and identify its domain and range of 2 1f x x
Domain: Range:0x 1y 0x x 0,
1y y
,1
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EXAMPLE 3EXAMPLE 3Using the graph, f(x) = , as a guide, describe the transformation, identify the domain and range, and graph the function, 4g x x
Domain:
Range:
4x
0y g(x)
g(x) translates 4 units right
x
4x x
0y y 4,
0,
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EXAMPLE 4EXAMPLE 4Using the parent function as a guide, describe the transformation, identify the domain and range, and graph the function, 4g x x
Domain: Range:0x 4y
g(x)
g(x) translates 4 units down
0x x
0, 4y y
4,
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YOUR TURNYOUR TURNUsing the parent function as a guide, describe the transformation, identify the domain and range, and graph the function, 5 5g x x
Domain: Range:
5x 5y
g(x)
g(x) translates 5 units left and 5 units down
5x x
5, 5,
5y y
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YOUR TURNYOUR TURNGraph each function and identify its domain and range of 2 1 3f x x
Domain:
Range:
1,
3,
g(x) translates 1 unit right, 3 units up and stretches by a factor of 2
1x
3y
1x x
3y y
Example 3: Applying Multiple Transformations
Reflect f across the x-axis, and translate it 4 units to the right.
••
Using the graph of as a guide, describe the transformation and graph the function .
f(x)= x
Lesson Quiz: Part II
g is f reflected across the y-axis and translated 3 units up.
Using the graph of as a guide, describe the transformation and graph the function .
•
•
gx = x + 3
g is f vertically stretched by a factor of 3, reflected across the x-axis, and translated 1 unit down.
●●
Check It Out! Example 3b
Using the graph of as a guide, describe the transformation and graph the function.
f(x)= x
g(x) = –3 x – 1
Example 4: Writing Transformed Square-Root Functions
Use the description to write the square-root
function g. The parent function is
reflected across the x-axis, compressed vertically
by a factor of , and translated down 5 units.
15
f(x)= x
Use the description to write the square-root function g.
Check It Out! Example 4
The parent function is reflected across the x-axis, stretched vertically by a factor of 2, and translated 1 unit up.
f(x)= x
Example 6: Graphing Radical Inequalities
x 0 1 4 9
y
Graph the inequality .
Step 1 Use the related equation to make a table of values.
y =2 x 3
Example 6 Continued
Step 2 Use the table to graph the boundary curve. The inequality sign is >, so use a dashed curve and shade the area above it.
Because the value of x cannot be negative, do not shade left of the y-axis.
Example 6 Continued
Check Choose a point in the solution region, such as (1, 0), and test it in the inequality.
0 > 2(1) – 3
0 > –1
Graph the inequality.
x –4 –3 0 5
y 0 1 2 3
Check It Out! Example 6a
Step 1 Use the related equation to make a table of values.
y = x+4
Step 2 Use the table to graph the boundary curve. The inequality sign is >, so use a dashed curve and shade the area above it.
Because the value of x cannot be less than –4, do not shade left of –4.
Check It Out! Example 6a Continued
Check Choose a point in the solution region, such as (0, 4), and test it in the inequality.
4 > (0) + 4
4 > 2
Check It Out! Example 6a Continued
Graph the inequality.
x –4 –3 0 5
y 0 1 2 3
Check It Out! Example 6b
Step 1 Use the related equation to make a table of values.
3y x 3
Step 2 Use the table to graph the boundary curve. The inequality sign is >, so use a dashed curve and shade the area above it.
Check It Out! Example 6b Continued
Check Choose a point in the solution region, such as (4, 2), and test it in the inequality.
2 ≥ 1
Check It Out! Example 6b Continued
Lesson Quiz: Part I
D:{x|x≥ –4}; R:{y|y≥ 0}
1. Graph the function and identify its range and domain.
•
Lesson Quiz: Part II
g is f reflected across the y-axis and translated 3 units up.
2. Using the graph of as a guide, describe the transformation and graph the function .
•
•
gx = x + 3
Lesson Quiz: Part III
3. Graph the inequality .
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