Name ________________________________________ Date __________________ Class__________________
LESSON
3-8
Reading Strategy
Use a Model
Just like quadratic and linear functions, polynomial functions can be
transformed. One type of transformation is reflection across the x- or y-axis.
You can reflect a graph by making its “mirror” image across the axis. Look
at the graph of f(x)  x 3  x 2  4, which is reflected across the y-axis.
The table shows rules for reflecting across the x-axis and the y-axis.
Transformation
Rule
Before Reflection
After Reflection
Reflection across
the x-axis
f (x)
f (x )  x 3  x 2  4
f (x)  (x 3  x 2  4)
Reflection across
the y-axis
f (x)
f (x )  x 3  x 2  4
f (x)  (x) 3  (x) 2  4
 x3  x2  4
 x 3  x 2  4
Answer each question.
1. a. Draw the graph of the polynomial
f (x)  x 3  x 2  4 reflected across the x-axis.

b. The point x, f ( x )
 is mapped to  x,  f ( x ) 
after reflection across the x-axis. Find the
point that is mapped to (1, 2) after reflection
across the x-axis.
_________________________________________
2. Write the function for each transformation of the polynomial.
Polynomial
a.
f (x )  x 3  4
b.
g(x)  6x 5  x 3  2
c.
h (x )  x 2  3 x  5
Reflect across x-axis
Reflect across y-axis
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3-66
Holt McDougal Algebra 2
2. a. g(x) = −2(0.25x)4 + 7(0.25x)2 − 4
4
2
b. g(x) = 4(−2x + 7x − 4)
4. f(x − 2) + 8
5. −f(x + 4) − 3
6. −f(x − 5) − 5
7. f(x + 3) + 4
Problem Solving
1. N(x) = 0.02x3 + 0.4x2 + 0.2x + 235
2. Vertical translation of 200 units up
3.
3. g(x) = −4(x + 2)3 + 5 4. g(x) = 20x3 − 4
5. g(x) = 12(x − 3)3 − 15
4. Because only positive values have
meaning in the context of the problem
6. 6 sin(x) + 1 ≈ 0.3x5 − x3 + 6x + 1
Reteach
5. An additional 200 cars are passing
through the intersection every week.
3
1. Up; g(x) = x + 3
6. Possible answer: R(x) = C(x) − 30;
vertical shift of 30 units down
7. 2C(x) = 0.04x3 + 0.8x2 + 0.4x + 70;
possible answer: a new mall opened at
the intersection.
Reading Strategies
1. a.
3
2. Right; g(x) = (x − 3) + 2
b. (1, −2)
2. a. f(x) = −x3 − 4; f(x) = −x3 + 4
3. Vertical stretch; g(x) = 4x4 − 12x2 + 8
b. g(x) = 6x5 + x3 − 2; g(x) = 6x5 + x3 + 2
4. Horizontal compression; g(x) = 32x4 −
24x2 + 4
c. h(x) = −x2 + 3x − 5; h(x) = x2 + 3x + 5
3-9 CURVE FITTING WITH POLYNOMIAL
Challenge
MODELS
1. f(x) + 11
Practice A
f(x − 2) + 27
−f(x) − 7
2. 0.5f(x)
3. −f(x) − 9
1. First
2. Third
3. Second
4. Second
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Holt McDougal Algebra 2