Transcript Document
8-7
Radical Functions
Warm Up
Identify the domain and range of each function.
1. f(x) = x2 + 2
D: R; R:{y|y ≥2}
2. f(x) = 3x3
D: R; R: R
Use the description to write the quadratic
2
function g based on the parent function f(x) = x .
3. f is translated 3 units up.
g(x) = x2 + 3
4. f is translated 2 units left.
g(x) =(x + 2)2
Holt Algebra 2
8-7
Radical Functions
Objectives
• Graph radical functions
• Transform radical functions by
changing parameters.
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
Radical Functions
8-7
x
–1
0
1
4
9
Holt Algebra 2
(x, f(x))
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
(x, f(x))
–8
(–8, –2)
–1
(–1,–1)
0
(0, 0)
1
(1, 1)
8
(8, 2)
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•
•
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•
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
–1
3
8
15
Holt Algebra 2
(x, f(x))
8-7
Radical Functions
Check It Out! Example 3
Graph each function, and identify its domain
and range.
x
(x, f(x))
–1
(–1, 0)
3
8
15
(3, 2)
(8, 3)
(15, 4)
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•
•
•
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
Using the graph of f(x)= x as a guide, describe
the transformation and graph the function.
g(x) = x + 1
Translate f 1 unit up.
Holt Algebra 2
•
•
8-7
Radical Functions
Check It Out! Example 5
Using the graph of f(x) = x as a guide, describe
the transformation and graph the function.
g is f vertically compressed
by a factor of
Holt Algebra 2
1
2
.
8-7
Radical Functions
General Equation
The general form of the square
root function is
y a xh k
The cube root function is
y a xh k
3
Holt Algebra 2
8-7
Radical Functions
Try these!
Using the graph of f(x)= x as a guide, describe
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.
The parent function f(x)= x is reflected across
the x-axis, stretched vertically by a factor of 2,
and translated 1 unit up.
Holt Algebra 2
8-7
Radical Functions
Check It Out! Example 6 Solution
Use the description to write the square-root
function g.
The parent function f(x)= x is reflected across
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
Holt Algebra 2
a = –2
8-7
Radical Functions
Check It Out! 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