Module 1 Test Review: Lesson 1.1 – 1.4 Analyzing Functions

Name ________________________________________ Date __________________ Class __________________
Module 1 Test Review: Lesson 1.1 – 1.4 Analyzing Functions
For 1–3, use the graph of the function 𝒇(𝒙).
1. Write the domain of the function as an inequality, using set notation and interval notation.
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2. Write the range of the function as an inequality, using set notation and interval notation.
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3. What is the range of the function if the domain is restricted to [−2,3]?
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4. A student reads 7 pages of a book every 4 minutes for 1 hour. Write a function that models this situation. Determine a domain
from the situation and identify the range. Use interval notation for the domain and range.
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Draw the graph of the f function with its given domain. Then determine the range using interval notation.
5. 𝑓(𝑥) = 3𝑥 − 4 with domain (−2, ∞):
Range: __________________________
6.The graph shows a function that models the number N of seniors from a high school accepted at a four-year university as a function
of time t in years over a ten-year period.
List the intervals that the function is decreasing.
Name ________________________________________ Date __________________ Class __________________
Module 1 Test Review: Lesson 1.1 – 1.4 Analyzing Functions
7.The table shows some values of a polynomial function.
x
0
1
2
3
4
g(x)
70
50
20
30
10
Find the average rate of change of the function over each of the following intervals.
A.
x = 1 to x = 2 _____________
8. A function is positive over the intervals
B. x = 1 to x = 4 _____________
{ x | 2  x  0} and { x | 3  x  }. What are the zeros for the function?
________________________
9. What are the zeros for the given function? _________________________
A fireworks projectile is launched at 10 meters per second from a 50 – meter cliff. The table shows the height, y, in
meters the projectile is above a field after x seconds. Use the table for problems 10 and 11.
Time (seconds)
0
1
2
3
4
5
Height (meters)
50
65
72
67
52
30
10. Find the equation of the line of best fit for the data in the table. ____________________________________
11. Predict the height after 3.5 seconds. ___________________________________________________________
Is this interpolation or extrapolation? Explain.
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12. Describe how to transform the graph of
________________
______________
f ( x )  x 2 to obtain the graph of the related function 𝑓(𝑥) = 7𝑓(−2𝑥) + 3.
_______________
_________________
Name ________________________________________ Date __________________ Class __________________
Module 1 Test Review: Lesson 1.1 – 1.4 Analyzing Functions
13.
14. Graph (𝑥) = 3𝑓(𝑥 + 1)2 − 4 given 𝑓(𝑥) = 𝑥 2 . State the domain and range.
Domain: __________________________
Range: ___________________________
15. Graph 𝑔(𝑥) = 𝑓(3𝑥) + 2 given 𝑓(𝑥) = 𝑥 2 . State the domain and range.
Domain : ____________________________
Range: _____________________________
16. Write g(x) in terms of f(x) after performing the given transformation of the graph of f(x).
Stretch the graph of f(x) vertically by a factor of 2, translate it to the left 1 units, up 2 units.
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Name ________________________________________ Date __________________ Class __________________
Module 1 Test Review: Lesson 1.1 – 1.4 Analyzing Functions
Find the inverse of the given functions.
17.
𝑓(𝑥) = 7𝑥 − 21
18.
𝑓(𝑥) =
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3𝑥−4
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2
Use composition to determine whether the pair of functions
are inverses.
𝑥
7
5
5
19. 𝑓(𝑥) = 5𝑥 − 7 and 𝑔(𝑥) = +
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20. The monthly cost C (in dollars) a cell phone carrier charges is C = .08m + 35 where m is the number of minutes used that exceed
300 minutes per month. Find an equation for the inverse function and interpret its meaning. List any restrictions on the domain and
range of the inverse function.
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21. Write the inverse of the function as a set of ordered pairs. Then plot the ordered pairs for the inverse on the grid.
𝑓(𝑥) = ( ___, ___ ), ( ___, ___ ), ( ___, ___ ),
( ___, ___ ), ( ___, ___ ), ( ___, ___ ),
𝑓 −1 (𝑥) = ( ___, ___ ), ( ___, ___ ), ( ___, ___ ),
( ___, ___ ), ( ___, ___ ), ( ___, ___ ),