Page 1 of 8
Algebra II
1-2 Study Guide: Introduction to Parent Functions
Attendance Problems
"
"
"
"
"
"
"
"
1. For the power ! 35 , identify the base and the exponent.
⎛ 2⎞
2. Evaluate ! ⎜ ⎟
⎝ 3⎠
−2
3. If ! f ( x ) = 2x + x , find f(9).
• I can identify parent functions from graphs and equations.
• I can use parent functions to model real-world data and make estimates for
unknown values.
"
Commone Core
CC.9-12.F.B.F.3 Build new functions from existing functions. Identify the effect on the
graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k
(both positive and negative); find the value of k given the graphs. Experiment with
cases and illustrate an explanation of the effects on the graph using technology. Include
recognizing even and odd functions from their graphs and algebraic expressions for
them.
CC.9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes.
CC.9-12.A.CED-2 Create equations that describe numbers or relationship. Create
equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
CC.9-12.A.CED-3 Create equations that describe numbers or relationship. Represent
constraints by equations or inequalities, and by systems of equations and/or inequalities,
and interpret solutions as viable or non-viable options in a modeling context. For
example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
"
Vocabulary: Parent function.
"
"
Page 2 of 8
Algebra II
4. (TPS) Refer to page 15, what is a parent function?
"
"
"
"
"
Parent Functions
Helpful Hint
To make graphs appear accurate on a graphing
calculator, use the standard square window. Press
ZOOM
ZOOM , choose 6:ZStandard, press ZOOM
again, and choose 5:ZSquare.
Video Example 1. Identify the parent function from its function rule.
Then graph g on your calculator and describe what transformation of
the parent function it represents.
A. g(x) = x - 1
B. ! g(x) = ( x + 4 )2
"
"
"
"
PLE
(0, c)
y-axis
(0, 0)
(0, 0)
(0, 0)
(0, 0)
Page 3 of 8
Algebra II
1
Identifying Transformations of Parent Functions
Identify the parent function for g from its function rule. Then graph g on
your calculator and describe what transformation of the parent function
it represents.
A g (x) = x + 5
g (x) = x + 5 is linear.
x has a power of 1.
The linear parent function f (x) = x
intersects the y-axis at the point (0, 0).
on a
tor,
Graph Y 1 = X + 5 on a graphing
calculator. The function g (x) = x + 5
intersects the y-axis at the point (0, 5).
ose
s
So g (x) = x + 5 represents a vertical
translation of the linear parent function
5 units up.
Identify the parent function for g from its function rule. Then graph g on
your calculator and describe what transformation of the parent function
it represents.
.
1-2 Introduction to Parent Functions
2
B g (x) = (x - 3)
g (x) = (x - 3)2 is quadratic. x - 3 has a power of 2.
The quadratic parent function f (x) = x 2
intersects the x-axis at the point (0, 0).
15
5/5/11 2:22:4
2
Graph Y 1 = (X - 3) on a graphing
calculator. The function g(x) = (x - 3)2
intersects the x-axis at the point (3, 0).
So g(x) = (x - 3)2 represents a
horizontal translation of the quadratic
parent function 3 units right.
"
"
"
"
"
"
Identify the parent function for g from its function rule. Then
graph g on your calculator and describe what transformation of
the parent function it represents.
1a. g(x) = x 3 + 2
It is often necessary to work with a set of data
points like the ones represented by the table
at right.
1b. g(x) = (-x)2
x
-4
-2
0
2
4
y
8
2
0
2
8
Page 4 of 8
Algebra II
Example 1. Identify the parent function for g from its function rule.
Then graph g on your calculator and describe what transformation of
the parent function it represents.
"
"
"
"
"
A. x - 3
B. ! g(x) = x 2 + 5
Guided Practice. Identify the parent function for g from its function
rule. Then graph g on your calculator and describe what transformation
of the parent function it represents.
"
"
"
"
"
"
"
"
"
6. ! g(x) = ( −x )
5. ! g(x) = x 3 + 2
2
It is often necessary to work with a set of data points like the ones represented by
the table.
x
y
–4
8
–2
2
0
0
2
2
4
8
With only the information in the table, it is impossible to know the exact behavior
of the data between and beyond the given points. However, a working knowledge
of the parent functions can allow you to sketch a curve to approximate those values
not found in the table.
"
Video Example 2. Graph the data from the table. Describe the
parent function and the transformation that best approximates
the data set.
"
"
"
"
"
"
"
"
6
at right.
With only the information in the table, it is impossible to know the exact
behavior of the data between and beyond the given points. However, a
Page 5 of 8
Algebraworking
II
knowledge of the parent functions can allow you to sketch a curve to
approximate those values not found in the table.
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
EXAMPLE
2
Identifying Parent Functions to Model Data Sets
Graph the data from the table. Describe the
parent function and the transformation that
best approximates the data set.
8
0
-4
-2
0
2
4
y
8
2
0
2
8
The graph of the data points resembles
the shape of the quadratic parent
function f (x) = x 2.
y
x
-4
x
4
The quadratic parent function passes
through the points (2, 4) and (4, 16). The
data set contains the points
(2, 2) = 2, 1 (4) and (4, 8) = 2, 1 (16) .
2
2
(
_
)
(
_
)
The data set seems to represent a vertical compression of the quadratic
parent function by a factor of __12 .
2. Graph the data from the table. Describe the parent function
Example 2. Graph the data
from this set of ordered pairs. Describe the parent
and the transformation that best approximates the data set.
function and the transformation that best
approximates the data set. x -4 -2 0 2 4
{(-2, 12), (-1, 3), (0, 0), (1,y3)-12
(2, 12)}
-6
0
6
12
"
"
"
Chapter 1 Foundations for Functions
"
"
"
SE612263_C01L02.indd 16
2/19/11 2:03:24
Page 6 of 8
Algebra II
7. Guided Practice. Graph the data from this
set of ordered pairs. Describe the parent
function and the transformation that best
approximates the data set.
"
"
"
"
"
"
"
"
"
x –4 –2 0
y –12 –6 0
2
6
4
12
Consider the two data points (0, 0) and (0, 1).
If you plot them on a coordinate plane you
might very well think that they are part of a
linear function. In fact they belong to each of the parent functions below.
"
"
"
"
"
"
"
"
"
"
Remember that any parent function you use to approximate a set of data should
never be considered exact. However, these function approximations are often
useful for estimating unknown values.
"
"
Page 7 of 8
Algebra II
Video Example 3. Graph the relationship height to
wind speed and identify which parent function best
describes it. Then use the graph to estimate the wave
height when the wind speed is 16 knots.
"
"
"
"
"
"
"
"
"
"
"
Example 3. Graph the relationship from year to sales in
millions of dollars and identify which parent function best
describes it. Then use the graph to estimate when cumulative
sales reached $10 million.
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
Year
1
2
3
4
5
Cumulative Sales
Sales (million $)
0.6
1.8
4.2
7.8
12.6
Algebra II
8. Guided Practice. The cost of playing an
online video game depends on the number
of months for which the online service is
used. Graph the relationship from number
of months to cost, and identify which
parent function best describes the data.
Then use the graph to estimate the cost of 5
months of online service.
"
"
"
"
"
1-2 Assignment
• (p 19) 17-20, 22, 28.
• Ready to Go Lesson 1A.
Page 8 of 8