Answers
5.
Chapter 1
4
1.1 Start Thinking
f(x) = x
As the string V gets wider, the points on the string
move closer to the x-axis. This activity mimics a
vertical shrink of a parabola.
−4
2.
y
4
Sample answer: The graph of f is a translation
3 units right of the parent linear function.
−2
2
4 x
−2
−4
−2
2
4 x
f(x) = x − 3
y
−4
2
2
−2
1.1 Warm Up
1.
y
6.
y
6
4 x
4
−2
−6
−4
g(x) = x 2 + 2
−4
3.
4.
y
−4
6
2
4
2
−2
2
4 x
y
4
−2
f(x) = x 2
The graph of g is a translation 2 units up of the
parent quadratic function.
7.
2
4 x
y
6
−4
−2
2 x
4
−4
f(x) = x 2
−2
1.1 Cumulative Review Warm Up
1. − 12
3. 12
2. 1
f(x) = (x − 1) 2
8.
1
3
h(x) = $ x + 4$
2
2. constant; The graph of f is a translation 1 unit up of
−6
the graph of the parent constant function.
3. a linear function
4
−4
−2
2 x
The graph of h is a translation 4 units left of the
graph of the parent function.
y
9.
h(x) = x + 2
6
f(x) = x
−4
y
6
followed by a translation 1 unit down
of the graph of the parent quadratic function.
4.
x
f(x) = $ x $
1. quadratic; The graph of f is a vertical shrink by a
factor of
4
The graph of f is a translation 1 unit right of the
graph of the parent quadratic function.
4. 25
1.1 Practice A
2
2
4 x
−2
−4
4
f(x) = 1
−4
y
f(x) = 5
2
−2
2
4 x
−2
Sample answer: The graph of h is a translation
2 units up of the graph of the parent linear function.
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All rights reserved.
The graph of f is a translation 4 units up of the
graph of the parent constant function.
Algebra 2
Answers
A1
Answers
18.
y
5.
f(x) = x 2
4
y
6
2
f(x) = x 2
4
−4
−2
5
g(x) = 3 x 2 + 2
−4
−2
2
2
4 x
−4
The graph of g is a vertical stretch by a factor of
19. Sample answer:
The graph of g is a reflection in the x-axis of the
graph of the parent quadratic function.
5
3
followed by a translation 2 units up of the graph of
the parent quadratic function.
y
6.
6
y
4
6
4
g(x) = $ x $ + 3
−2
f(x) = x 2
f(x) = (x + 2) 2
2
−4
4 x
g(x) = −x 2
−2
−4
f(x) = $ x $
2
4 x
The graph of g is a translation 3 units up of the
graph of the parent absolute value function.
−2
2
4 x
The graph of f is a translation 2 units left of the
graph of the parent quadratic function.
7.
4
1.1 Practice B
y
2
1. absolute value; The graph of f is a vertical shrink by
2
5
a factor of
−4
followed by a translation 3 units right
−2
2
f(x) = $ x $
of the graph of the parent absolute value function.
4 x
h(x) = $ x$ − 2
−4
2. linear; The graph of f is a vertical stretch by a factor
of 2 followed by a translation 1 unit up of the graph
of the parent linear function.
3.
4
y
The graph of h is a translation 2 units down of the
graph of the parent absolute value function.
8.
h(x) = x + 2
4
f(x) = 1
f(x) = x
−4
2
4 x
2
−2
2
−2
−2
−4
−4
Sample answer: The graph of h is a translation
2 units up of the graph of the parent linear function.
4.
−4
4
y
4 x
f(x) = −3
The graph of f is a translation 4 units down of the
parent constant function.
y
2
f(x) = −x
−4
f(x) = x
−2
2
4 x
−2
−4
Sample answer: The graph of f is a reflection in the
x-axis of the graph of the parent linear function.
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All rights reserved.
Algebra 2
Answers
A3
Answers
9.
4
13.
y
y
6
2
f(x) = x
−4
4
−2
2
4 x
3
f(x) = x
5
−2
2
−4
Sample answer: The graph of f is a vertical shrink
by a factor of 53 of the graph of the parent linear
3
h(x) = 2 #x#
y
4
4
14.
4
y
2
f(x) = # x #
4
−4
2
2
2
4 x
The graph of f is a reflection in the x-axis, followed
by a translation 2 units left and 13 units down of the
value function.
graph of the parent absolute value function.
y
15. absolute value; domain: all real numbers, range:
y ≥ 3
6
4
4
h(x) = 3 x 2
16. linear; domain: all real numbers, range: all real
numbers
2
f(x) = x 2
−4
−2
2
17. quadratic; domain: all real numbers, range:
4 x
The graph of h is a vertical stretch by a factor of
y ≥ −3
4
3
18. a. quadratic function
of the graph of the parent quadratic function.
12.
8
1
3
−4
Sample answer: The graph of h is a vertical stretch
by a factor of 32 of the graph of the parent absolute
11.
4 x
f(x) = −# x + 2# −
f(x) = #x#
−2
4
9
units up of the graph of the parent quadratic
function.
6
−4
x
h(x) = (x − 5) 2 + 9
The graph of h is a translation 5 units right and
function.
10.
2
f(x) = x 2
b. 0; t is the number of seconds after the ball is
thrown, so when the ball is thrown t = 0.
y
c. 6 ft; f (0) = 6
6
2
−4
−2
1.1 Enrichment and Extension
1
g(x) = 10 x 2 + 5
4
1.
2
f(x) = x 2
2
4 x
The graph of g is a vertical shrink by a factor of
−6 B′ −4
1
10
followed by a translation 5 units up of the graph of
the parent quadratic function.
A4
Algebra 2
Answers
y
A′
A
B
C′
D
2
C
6 x
D′
Sample answer: Trapezoid A′B ′C ′D ′ a reflection in
the x-axis, followed by translation 1 unit down and
6 units left of trapezoid ABCD.
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All rights reserved.
Answers
7. g ( x ) = − 5 + − x + 8
9. g ( x) = 3 − 12 x
8. g ( x ) = − 4 x − 1 + 2
10. g ( x) = x + 53
11. g ( x ) = 9 x + 2
12. g ( x ) = − 4 x − 2 + 8
13. g ( x) = 14 x + 54
14. g ( x ) = − x + 2
1.3 Start Thinking
You can model this situation with the equation
y = 14.99 x − 8.50 x, where x represents the number
of units sold and y represents the total profit. You are
looking for the point that has a y-value of 150,000. By
substituting 150,000 for y in the equation and solving
for x, you obtain x = 23,113.
New Product
1.2 Enrichment and Extension
y
1. g ( x ) = 2 x − 8; x = 4
(23,113, 150,000)
Profit
150,000
2. g ( x) = − 2 x − 1; x = − 12
100,000
50,000
3. g ( x ) = 6 x − 6; x = 1
0
0
9,000
4. g ( x) = 6 x + 4; x = − 23
1. D = {0 ≤ x ≤ 82}
6. g ( x ) = − 2 x − 6; x = − 3
7. g ( x ) = x − 1 − 2; x = 3, x = −1
8. g ( x ) = x + 3 + 1; no solution, does not intersect
x-axis
10. g ( x ) = 2 x + 1 − 6; x = 2, x = − 4
19
2
12. g ( x) = − 12 x − 3 + 2; x = 7, −1
JAMES MONROE
R = {0 ≤ y ≤ 12,300,000}
2. D = {0 ≤ x ≤ 5}
R = {0 ≤ y ≤ 4220}
3. D = {0 ≤ x ≤ 2500}
9. g ( x ) = − x + 5 ; x = − 5
1.2 Puzzle time
27,000 x
1.3 Warm Up
5. g ( x) = 4 x − 14; x = 72
11. g ( x) = − 4 x − 38 ; x =
18,000
Product sold
R = {0 ≤ y ≤ 13,125}
1.3 Cumulative Review Warm Up
1. 5.1
2. 9.3
3. 10.3
4. $130,533.30
1.3 Practice A
3 x; The sales tax rate is 3 = 6%.
1. y = 50
50
2. y = − 12 x + 10; An amount of 12 ounce of soap is
used each day.
3. Soapy Car Wash; 6 extras
4. not linear
5. yes; y = 12 x; y = 7.5; This means 7.5 cars are
washed in 15 minutes.
6. yes; A correlation coefficient close to −1 is a
strong, negative correlation.
A6
Algebra 2
Answers
Copyright © Big Ideas Learning, LLC
All rights reserved.
Notes&1.3&Modeling&with&Linear&Functions&
&
Lines&
Given&two&points&on&a&line& ( x1 , y1 ) and ( x2 , y2 ) &the&slope&of&the&line&is:&& m =
y2 − y1
&
x2 − x1
&
The&equation&of&a&line&in&slope&intercept&form&is:&& y = mx + b &or& f ( x) = mx + b &
&
The&equation&of&a&line&in&point8slope&form&is:&& y − y1 = m( x − x1 ) &
&
Examples:&
1.)&&The&graph&shows&the&remaining&balance&y&on&a&car&loan&after&making&x&monthly&payments.&&Write&an&equation&
of&the&line&and&interpret&the&slope&and&the&y8intercept.&&What&is&the&remaining&balance&after&36&payments?&
&
&
&
&
&
&
&
&
&
2.)&&Donna&and&Kim&are&both&babysitters.&&Donna&charges&a&flat&fee&of&$10&plus&$6&per&hour&to&babysit.&&The&table&
shows&the&total&hourly&fee&that&Kim&charges&to&babysit.&&Who&charges&more&per&hour?&&How&many&hours&must&Kim&
and&Donna&babysit&for&their&total&fees&to&be&the&same?&
&
&
&
&
&
&
&
3.)&&The&table&shows&the&amount&of&fruit&used&to&make&a&smoothie&(in&ounces)&and&the&total&cost&(in&
dollars)&of&the&smoothie.&&Does&the&data&show&a&linear&relationship?&&If&so,&write&an&equation&of&a&line&of&
fit&and&use&it&to&estimate&the&total&cost&of&a&smoothie&that&is&made&using&8&ounces&of&fruit.&
&
&
ANSWERS
1. linear; The graph is a vertical shrink
by a factor of —13 followed by a
translation 1 unit down of the parent
linear function.
2. quadratic; The graph is a vertical
stretch by a factor of 2 followed by
a translation 1 unit left of the parent
quadratic function.
3. absolute value; The graph is a
translation 1 unit left and 2 units
down of the parent absolute value
function.
4. The graph of f is a translation —12 unit
up of the parent constant function.
4
y
−4
Identify the function family to which g belongs. Compare the graph of the function to the graph of its
parent function. (Section 1.1)
1.
x
5. The graph of f is a vertical stretch
by a factor of 3 of the parent linear
function.
y
2
3.
y
g(x) = "x + 1" −2 4
8
−2
4
x
2
4
−4
−2
−4
y
−2
2
2
x
x
g(x) = 2(x + 1)2
Graph the function and its parent function. Then describe the transformation. (Section 1.1)
3
4. f(x) = —2
5. f(x) = 3x
8. f(x) =
1
—4 x 2
6. f(x) = 2(x − 1)2
1
+1
9. f(x) = −—2 x − 4
10. f(x) = 2x + 1; translation 3 units up
11. f(x) = −3∣ x − 4 ∣; vertical shrink by a factor of —2
12. f(x) = 3∣ x + 5 ∣; reflection in the x-axis
13. f(x) = —3 x − —3 ; translation 4 units left
1
1
2
Write a function g whose graph represents the indicated transformations of the graph of f. (Section 1.2)
2
14. Let g be a translation 2 units down and a horizontal shrink by a factor of —3 of the graph
of f(x) = x.
of f(x) = x.
y=x
−2
2
4
16. Let g be a reflection in the x-axis and a vertical stretch by a factor of 4 followed by a
translation 7 units down and 1 unit right of the graph of f(x) = ∣ x ∣.
x
17. Let g be a translation 1 unit down and 2 units left followed by a vertical shrink by a factor
of —12 of the graph of f(x) = ∣ x ∣.
f(x) = 3x
18. The table shows the total distance a new car travels each month after it is purchased.
−4
What type of function can you use to model the data? Estimate the mileage after
1 year. (Section 1.1)
6. The graph of f is a vertical stretch by
a factor of 2 followed by a translation
1 unit right of the parent quadratic
function.
Time (months), x
0
2
5
6
9
Distance (miles), y
0
2300
5750
6900
10,350
19. The total cost of an annual pass plus camping for x days in a National Park can be
modeled by the function f(x) = 20x + 80. Senior citizens pay half of this price and
receive an additional $30 discount. Describe how to transform the graph of f to model
the total cost for a senior citizen. What is the total cost for a senior citizen to go camping
for three days? (Section 1.2)
y
2
f(x) = 2(x − 1)
−4
g(x) = 3 x − 1
15. Let g be a translation 9 units down followed by a reflection in the y-axis of the graph
2
y = x2
12
1
4
−4
2.
y
Write a function g whose graph represents the indicated transformation of the graph of f. (Section 1.2)
2 y =41
−2
Quiz
7. f(x) = −∣ x + 2 ∣ − 7
3
f(x) = 2
2
1.1–1.2
−2
2
4
2
20
6 x
Chapter 1
Linear Functions
−2
7. The graph of f is a reflection across
the x-axis followed by a translation
2 units left and 7 units down of the
parent absolute value function.
8
−8
HSCC_Alg2_PE_01.MC.indd 20
10
y
y = x2
4
−12
8. The graph of f is a vertical shrink by a factor
of —14 followed by a translation 1 unit up of the
parent quadratic function.
8
y = "x"
−4
4
8
6
12 x
4
−4
−6
−4
−2
2
−2
20
Chapter 1
1 2
f(x) = 4 x + 1
2
f(x) = −"x + 2" − 7
−12
y
4
6 x
9. See Additional Answers.
10. g(x) = 2x + 4
3
11. g(x) = −—2 ∣ x − 4 ∣
12. g(x) = −3∣ x + 5 ∣
2
13. g(x) = —13 (x + 4) − —3
14.
15.
16.
17.
18.
19.
g(x) = —32 x − 2
g(x) = − x − 9
g(x) = −4∣ x − 1 ∣ − 7
1
g(x) = —12 ∣ x + 2 ∣ − —2
linear; 13,800
See Additional Answers.
2/20/14 9:14 AM