Download Algebra 2AB sample chapter 4 exam problems

Name: ______________________ Class: _________________ Date: _________
Chapter 4 sample exam problems ALL
Graph the function and its parent function. Then describe the transformation.
____
1. g(x) =
2
x
3
a.
c.
The graph of g is a vertical
stretch and a reflection in the x-axis of the
parent linear function.
b.
The graph of g is a vertical stretch of the
parent linear function.
d.
The graph of g is a vertical
shrink and a reflection in the x-axis of the
parent linear function.
The graph of g is a vertical shrink of the
parent linear function.
1
ID: A
Name: ______________________
____
ID: A
2. g(x) = −3 (x − 3 ) + 2
2
a.
c.
The graph of g is a translation 3 units
left, a vertical stretch,
a reflection in the x -axis, and a
translation 2 units down of the parent
quadratic function.
The graph of g is a translation 3 units
right, a vertical stretch, and a translation
2 units up of the parent quadratic
function.
d.
b.
The graph of g is a translation 3 units
left, a vertical stretch,
a reflection in the x -axis, and a
translation 2 units up of the parent
quadratic function.
The graph of g is a translation 3 units
right, a vertical stretch,
a reflection in the x -axis, and a
translation 2 units up of the parent
quadratic function.
Write a function g whose graph represents the indicated transformation of the graph of f.
____
3. f(x) = |x + 4 | − 2 ; translation 7 units right
a. g(x) = − |x − 3 | − 2
b. g(x) = |x + 4 | + 11
c.
d.
2
g(x) = |x − 3 | − 2
g(x) = − |x + 4 | + 11
Name: ______________________
____
4. f(x) =| x|
a.
b.
____
ID: A
g(x) = |x + 3 | + 1
g(x) = − |x + 3 | + 1
c.
d.
g(x) = − |x + 1 | + 3
g(x) = |x + 1 | + 3
5. Select the statements that are true for modeling data with linear equations.
a. The line of best fit is the line that lies as close as possible to all of the data points.
b. A correlation coefficient near –1 indicates that the points lie close to a line with
a negative slope.
c. The correlation coefficient is the slope of the line of fit.
d. The relationship between two quantities can always be represented with a linear model.
e. Data in a scatter plot that show an approximately linear relationship can never be
modeled with a linear equation.
f. A correlation coefficient near 0 indicates that the points do not lie close to any line.
6. Identify the function family to which f(x) = 2| x + 2|− 3 belongs. Compare the graph of f to the graph of its
parent function.
3
Name: ______________________
ID: A
Write an equation of the line and interpret the slope.
7.
Find the domain and range of the function represented by the graph.
____
8.
a.
b.
c.
d.
domain: −4 ≤ x ≤ 2,
domain: −4 < x < 2,
domain: −4 ≤ x ≤ 4,
domain: −4 < x < 4,
range: −4 ≤ y ≤ 4
range: −4 < y < 4
range: −4 ≤ y ≤ 2
range: −4 < y < 2
4
Name: ______________________
____
ID: A
9. Let f(x) = 2x − 3 and g(x) = f(x + 3) . Use the graphs of f and g to describe the transformation from the graph
of f to the graph of g.
a.
b.
vertical translation 3 units down
horizontal translation 3 units right
c.
d.
5
vertical translation 3 units up
horizontal translation 3 units left
Name: ______________________
ID: A
Graph the function. Compare the graph to the graph of f(x) = | x |. Describe the domain and range.
____ 10. g(x) = | x | − 2
a.
c.
translation 2 units down
domain: all real numbers
range: y ≥ −2
translation 2 units down
domain: all real numbers
range: all real numbers
b.
d.
translation 2 units up
domain: all real numbers
range: all real numbers
translation 2 units up
domain: all real numbers
range: y ≥ 2
6
Name: ______________________
ID: A
____ 11. g(x) = −3 | x |
a.
c.
g is a vertical stretch of the graph of f by
a factor of 3.
domain: all real numbers
range: y ≥ 0
b.
g is a vertical stretch of the graph of f by
a factor of 3 and a reflection in the
x-axis.
domain: all real numbers
range: y ≤ 0
d.
g is a vertical shrink of the graph of f by
1
a factor of .
3
domain: all real numbers
range: y ≥ 0
g is a vertical shrink of the graph of f by
1
a factor of and a reflection in the
3
x-axis.
domain: all real numbers
range: y ≤ 0
7
Name: ______________________
ID: A
Describe the transformations from the graph of f(x) = |x | to the graph of the given function. Then
graph the given function.
____ 12. g(x) = − | x − 1 | − 2
a.
The transformations are a
horizontal translation 1 unit left,
then a reflection in the x-axis,
then a vertical translation 2 units up.
c.
The transformations are a
horizontal translation 1 unit left,
then a reflection in the x-axis,
then a vertical translation 2 units down.
b.
The transformations are a
horizontal translation 1 unit right,
then a reflection in the x-axis,
then a vertical translation 2 units down.
d.
The transformations are a
horizontal translation 1 unit right,
then a reflection in the x-axis,
then a vertical translation 2 units up.
8
Name: ______________________
ID: A
____ 13. g(x) = |4x + 1 | + 3
a.
The transformations are a horizontal
translation 1 unit left, then a horizontal
stretch by a factor of 4, then a vertical
translation 3 units up.
c.
The transformations are a horizontal
translation 1 unit left, then a horizontal
1
shrink by a factor of , then a vertical
4
translation 3 units down.
b.
The transformations are a horizontal
translation 1 unit right, then a horizontal
1
shrink by a factor of , then a vertical
4
translation 3 units up.
d.
The transformations are a horizontal
translation 1 unit left, then a horizontal
1
shrink by a factor of , then a vertical
4
translation 3 units up.
____ 14. Consider the parent function f(x) = |x | . Which transformations occurred to create g(x) = −5 |x − 3 | − 6 ?
a. horizontal translation 3 units right
e. vertical translation 6 units down
b. reflection in the x-axis
f. vertical translation 6 units up
c. vertical stretch by a factor of 5
g. reflection in the y-axis
d. horizontal stretch by a factor of 5
h. horizontal translation 3 units left
9
Name: ______________________
ID: A
Let f(x) = 3x + 1. Match the transformed function below with its description.
a. reflection in the x-axis
e. vertical stretch by a factor of 5
1
f. horizontal translation 5 units right
b. horizontal shrink by a factor of
2
1
c. vertical translation 2 units up
g. vertical shrink by a factor of
5
d. reflection in the y-axis
h. horizontal stretch by a factor of 2
____ 15. h(x) = 3(x − 5) + 1
16. The graph shows the total cost c of a T-shirt order from Custom T’s when you order x custom printed
T-shirts.
Custom T’s
The table shows sample costs from a different vendor, Shirts and More.
Shirts and More
Number of
Total Cost
T-Shirts
9
$98
18
$161
27
$224
If your school’s Entrepreneurs Club needs 45 T-shirts, which vendor would you use? Explain.
10
ID: A
Chapter 4 sample exam problems ALL
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
D
D
C
B
A, B, F
absolute value; The graph is a vertical stretch and a translation 2 units left and 3 units down.
The domain of each function is all real numbers, but the range of f is y ≥ −3 and the range of
the parent function is y ≥ 0.
y = 6x; The runner travels 6 miles each hour spent running.
A
D
C
C
B
D
A, B, C, E
F
Custom T's; The cost is lower. From the graph, Custom T’s total cost is $250. Based on the table, Shirts and
More’s total cost is $350.
1
Chapter 4 sample exam problems ALL [Answer Strip]
D
__________
2.
B
__________
4.
D
__________
1.
A, B, F
__________
5.
C
__________
3.
ID: A
Chapter 4 sample exam problems ALL [Answer Strip]
D
__________
9.
C
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10.
A
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8.
ID: A
Chapter 4 sample exam problems ALL [Answer Strip]
C
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11.
D
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13.
B
__________
12.
A, B, C, E 14.
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ID: A
Chapter 4 sample exam problems ALL [Answer Strip]
F
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15.
ID: A