8-7 Radical Functions
Identify the domain and range of each function.
1. f(x) = x 2 + 2 D: R ; R:{y|y ≥2}
2. f(x) = 3x 3 D: R ; R: R
Use the description to write the quadratic function g based on the parent function f(x) = x 2 .
3. f is translated 3 units up.
g(x) = x 2 + 3
4. f is translated 2 units left.
g(x) =(x + 2) 2
Holt Algebra 2

8-7 Radical Functions
Holt Algebra 2

8-7 Radical Functions
Check It Out!
Example 1
Make a table of values. Plot enough ordered pairs to see the shape of the curve. Choose both negative and positive values for x if possible.
Holt Algebra 2

8-7 Radical Functions
(x, f(x)) x
–1
0
1
4
9
Holt Algebra 2

8-7 Radical Functions
Holt Algebra 2

8-7 Radical Functions
Check It Out!
Example 2
Make a table of values. Plot enough ordered pairs to see the shape of the curve. Choose both negative and positive values for x if possible.
Holt Algebra 2

8-7 Radical Functions
Check It Out!
Example 2 Continued x
–8
–1
0
1
8
(x, f(x))
( –8, –2)
( –1,–1)
(0, 0)
(1, 1)
(8, 2)
•
•
•
•
•
The domain is the set of all real numbers. The range is also the set of all real numbers.
Holt Algebra 2

8-7 Radical Functions
Check It Out!
Example 3
Graph each function, and identify its domain and range.
(x, f(x)) x
–1
3
8
15
Holt Algebra 2

8-7 Radical Functions
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Example 3
Graph each function, and identify its domain and range.
x
–1
3
8
15
(x, f(x))
( –1, 0)
(3, 2)
(8, 3)
(15, 4)
•
•
•
•
The domain is {x|x ≥ –1}, and the range is {y|y ≥0}.
Holt Algebra 2

8-7 Radical Functions
The graphs of radical functions can be transformed by using methods similar to those used to transform linear, quadratic, polynomial, and exponential functions. This lesson will focus on transformations of square-root functions.
Holt Algebra 2

8-7 Radical Functions
Holt Algebra 2

8-7 Radical Functions
Check It Out!
Example 4 f(x)= x the transformation and graph the function.
g(x) = x + 1
Translate f 1 unit up .
•
Holt Algebra 2

8-7 Radical Functions
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Example 5 f(x) = x the transformation and graph the function.
g is f vertically compressed by a factor of .
2
Holt Algebra 2

8-7 Radical Functions
y
 a x
  k
y
 a x
  k
Holt Algebra 2

8-7 Radical Functions
Try these!
f(x)= x the transformation and graph the function. g(x) = –3 x – 1
g is f vertically stretched by a factor of 3, reflected across the x-axis, and translated
1 unit down.
●
●
Holt Algebra 2

8-7 Radical Functions
Check It Out!
Example 6
Use the description to write the square-root function g.
f(x)= x the x-axis, stretched vertically by a factor of 2, and translated
1 unit up.
Holt Algebra 2

8-7 Radical Functions
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Example 6 Solution
Use the description to write the square-root function g.
f(x)= x the x-axis, stretched vertically by a factor of 2, and translated
1 unit up.
Step 1 Identify how each transformation affects the function.
Reflection across the x-axis: a is negative
Vertical compression by a factor of 2
Translation 1 unit up: k = 1
a = –2
Holt Algebra 2

8-7 Radical Functions
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Example 6 Continued
Step 2 Write the transformed function.
Substitute –2 for a and 1 for k.
Simplify.
Check Graph both functions on a graphing calculator.
The g indicates the given transformations of f.
Holt Algebra 2