Download Holt McDougal Algebra 2 - Effingham County Schools

Radical Functions
Objectives
Graph radical functions and
inequalities.
Transform radical functions by
changing parameters.
Vocabulary
radical function
square-root function
Holt McDougal Algebra 2
Radical Functions
Example 1A: Graphing Radical Functions
Graph each function and identify its domain
and range.
x
(x, f(x))
3
4
7
12
The domain is {x|x
Holt McDougal Algebra 2
}, and the range is {y|
}.
Radical Functions
Check It Out! Example 1a
Graph each function and identify its domain
and range.
x
(x, f(x))
–8
–1
0
1
8
The domain is {x|x
Holt McDougal Algebra 2
}, and the range is {y|
}.
Radical Functions
Check It Out! Example 1a Continued
Check Graph the function on a graphing calculator.
Holt McDougal Algebra 2
Radical Functions
Example 1B: Graphing Radical Functions
Graph each function and identify its domain
and range.
x
(x, f(x))
–6
1
2
3
10
The domain is {x|x
Holt McDougal Algebra 2
}, and the range is {y|
}.
Radical Functions
Example 1B Continued
Check Graph the function on a graphing calculator.
Holt McDougal Algebra 2
Radical Functions
Check It Out! Example 1b
Graph each function, and identify its domain
and range.
x
(x, f(x))
–1
3
8
15
The domain is {x|x
Holt McDougal Algebra 2
}, and the range is {y|y
}.
Radical Functions
Holt McDougal Algebra 2
Radical Functions
Example 2: Transforming Square-Root Functions
Using the graph of f(x) = x as a guide, describe
the transformation and graph the function.
g(x) =
x+5
Holt McDougal Algebra 2
Radical Functions
Check It Out! Example 2a
Using the graph of f(x)= x as a guide, describe
the transformation and graph the function.
g(x) = x + 1
Holt McDougal Algebra 2
Radical Functions
Check It Out! Example 2b
Using the graph of f(x) = x as a guide, describe
the transformation and graph the function.
Holt McDougal Algebra 2
Radical Functions
Example 3: Applying Multiple Transformations
Using the graph of f(x)= x as a guide, describe
the transformation and graph the function
.
Holt McDougal Algebra 2
Radical Functions
Example 3: Applying Multiple Transformations
Using the graph of f(x)= x as a guide, describe
the transformation and graph the function
.
Reflect f across the
x-axis, and translate it
4 units to the right.
Holt McDougal Algebra 2
•
•
Radical Functions
Check It Out! Example 3a
Using the graph of f(x)= x as a guide, describe
the transformation and graph the function.
Holt McDougal Algebra 2
Radical Functions
Check It Out! Example 3a
Using the graph of f(x)= x as a guide, describe
the transformation and graph the function.
g is f reflected across the
y-axis and translated 3
units up.
●
●
Holt McDougal Algebra 2
Radical Functions
Check It Out! Example 3b
Using the graph of f(x)= x as a guide, describe
the transformation and graph the function.
g(x) = –3 x – 1
Holt McDougal Algebra 2
Radical Functions
Check It Out! Example 3b
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 McDougal Algebra 2
●
●
Radical Functions
Example 4: Writing Transformed Square-Root
Functions
Use the description to write the square-root
function g. The parent function f(x)= x is
reflected across the x-axis, compressed vertically
by a factor of 1 , and translated down 5 units.
5
Holt McDougal Algebra 2
Radical Functions
Check It Out! Example 4
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 McDougal Algebra 2
Radical Functions
Example 6: Graphing Radical Inequalities
Graph the inequality
.
Step 1 Use the related equation y =2 x -3 to
make a table of values.
x
y
Holt McDougal Algebra 2
0
1
4
9
Radical Functions
Check It Out! Example 6a
Graph the inequality.
Step 1 Use the related equation y =
make a table of values.
x
y
Holt McDougal Algebra 2
–4
–3
0
5
x+4 to
Radical Functions
Check It Out! Example 6b
Graph the inequality.
Step 1 Use the related equation y =
make a table of values.
x
y
Holt McDougal Algebra 2
–4
–3
0
5
3
x - 3 to
Radical Functions
Lesson Quiz: Part I
1. Graph the function
range and domain.
D:{x|x
and identify its
}; R:{y|y
}
2. Using the graph of
as a guide, describe the
transformation and graph the function g(x) = -x + 3 .
Holt McDougal Algebra 2