Mid Term Review

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Mid Term Review
I. Foundation of Functions
Find the inverse of:
1. 𝑦 = 11𝑥 + 6
2. 𝑦 = 3𝑥 − 21
Use compositions to determine if these functions are inverses:
𝑥−9
5. 𝑓(𝑥) = 2𝑥 + 10 and 𝑔(𝑥) = 12𝑥 + 5
4. 𝑓(𝑥) = 4𝑥 + 9 and 𝑔(𝑥) = 4
Answer the following word problems.
6. A student bought concert tickets online. The cost, 𝑐 in dollars, of tickets, 𝑡, can be
found using the function 𝑐 = 25𝑡 + 13.50. If the student spent a total of $88.50 on this
ticket purchase, how many tickets did he buy?
7. The Spanish Club is ordering t-shirts online. The cost, 𝑐 in dollars, of t-shirts, 𝑡, can
be found using the function 𝑐 = 11𝑡 + 27. If the club spent a total of $159.00 on this tshirt order, how many t-shirts did the club buy?
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Use the following graph for #8-9.
The graph shows the relationship between the number of students who are sleeping
and the number of minutes since class started.
8. What does the x-intercept of the graph represent? ___________________________
9. What does the y-intercept of the graph represent? ___________________________
Use the following table for #10-11.
Lily is driving a car at a constant speed. The table below shows the total number of
miles driven as a function of the hours spent driving.
Hours Spent
Miles Driven
Driving
2
114
4
228
6
342
10. Based on the data in the table, how many miles has Lily driven in 7 hours?
11. Based on the data in the table, how many miles has Lily driven in 8 hours?
Which function below represents the data in the table?
12. _____
13. _______
x
Y
x
y
1
7
1
1.5
2
9
2
5
3
11
3
8.5
4
13
4
12
5
15
5 15.5
A. 𝑦 = 2𝑥 + 5
A. 𝑦 = 3.5𝑥 2 − 2
B. 𝑦 = 2(5𝑥 )
B. 𝑦 = 3.5(2𝑥 )
2
C. 𝑦 = 2𝑥 + 5
C. 𝑦 = 2𝑥-3.5
1
D. 𝑦 = 2𝑥+5
D. 𝑦 = 3.5𝑥 − 2
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II. Absolute value equations and inequalities
14. Graph the absolute value function
function
1
𝑓(𝑥) = 4 │𝑥 − 4│ + 5
15. Graph the absolute value
1
𝑓(𝑥) = 2 │𝑥 + 2│ − 4
16. Analyze the domain of the absolute value function.
17.
A.
{𝑥| 𝑥 < −5}
Write the domain and range of
B.
{𝑥│ − ∞ < 𝑥 < ∞}
the above absolute value function
C.
{𝑥│𝑥 ≥ −5}
D:_______________
D.
{𝑥│ − 7 ≤ 𝑥 ≤ 10}
R:_______________
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Analyze the range of the absolute value function:
18.
𝑓(𝑥) = − ⎸𝑥 + 2 ⎸ + 4
A.
B.
C.
D.
𝑦
𝑦
𝑦
𝑦
19.
≥4
<2
≤4
< −2
A.
B.
C.
D.
𝑓(𝑥) = ⎸𝑥 − 8 ⎸ − 11
𝑦 ≥ −11
𝑦 < −11
𝑦 ≤ 11
𝑦<8
20. Which of the following absolute value functions have a maximum?
1
I. 𝑓(𝑥) = ⎸𝑥 − 3 ⎸ − 2
II. 𝑓(𝑥) = − 2 ⎸𝑥 + 5 ⎸
III. 𝑓(𝑥) = − ⎸𝑥 ⎸ − 1
IV. 𝑓(𝑥) = 4 ⎸𝑥 − 3 ⎸
A. I and III
1
B. II and III
C. II only
D. I and IV
21. Which of the following absolute value functions have a minimum?
II. 𝑓(𝑥) = − 2 ⎸𝑥 + 5 ⎸
III. 𝑓(𝑥) = − ⎸𝑥 ⎸ − 1
IV. 𝑓(𝑥) = 4 ⎸𝑥 − 3 ⎸
A. I and IV
22.
1
I. 𝑓(𝑥) = ⎸𝑥 − 3 ⎸ − 2
1
B. II and III
C. IV only
D. All of the above
Fill in the blank: The absolute value parent function is symmetric about the __-axis.
23. Which function represents the graph?
A.
𝑦 = − ⎸𝑥 − 2 ⎸ − 10
B.
𝑦 = − ⎸𝑥 + 2 ⎸ + 10
C.
𝑦 = − ⎸𝑥 − 10 ⎸ + 2
D.
𝑦 = − ⎸𝑥 + 10 ⎸ − 2
24. Write the function which represents the
graph?
_______________________
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25. While playing pool, you try to shoot the eight ball into the corner pocket as
shown. Imagine that a coordinate plane is placed over the pool table. The eight
5
ball is at (5, 4) and the pocket you are aiming for is at (10, 5). You are going to
bank the ball off the side at (6, 0).
Show all the work when writing the absolute value function that represents the
path of the ball.
26. Solve: |4𝑥 − 5| = 7
27. Solve: 3|𝑥 + 11| = 6
28. Solve: |10𝑥| − 15 = 25
29. Solve: |𝑥 + 3| + 8 = 14
A. 30, 50
B. -50, 30
C. -1, 1
D. -4, 4
A. -2, 2
B. -9, 3
C. 19, 25
D. No solution
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30. Solve the following inequality:
⎸2𝑥 − 4 ⎸ + 5 < 11
A. 𝑥 < −1 or 𝑥 > 5
B. 𝑥 < 5
C. −1 < 𝑥 < 5
D. 2 < 𝑥 < 4
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31. Solve the following inequality:
⎸4𝑥 + 4 ⎸ + 2 > 14
A. 𝑥 < −4 or 𝑥 > 2
B. 𝑥 > 4
C. −4 < 𝑥 < 2
D. 𝑥 = 4
III. Quadratic equations and inequalities
32. Write a function that has a vertex of (2,4) and contains the point (4,16).
33. Write a function that has a vertex of (-4,-2) and contains the point (-2,18).
34. Given the vertex and point, find the equation of the function
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35. Given the vertex and point, find the equation of the function
36. Solve the quadratic equation using the square root method: (𝑥 − 3)2 + 15 = 45.
37. Solve the quadratic equation using the square root method: (𝑥 + 5)2 + 12 = 76.
38. Solve the quadratic equation using the square root method: 5𝑥 2 + 56 = 156.
39. Solve the quadratic equation using the square root method: 2𝑥 2 − 36 = 132.
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40. Which statement about the quadratic equation is true?
−5.5𝑥 2 + 198 = 0
A.
B.
C.
D.
The equation has a x=6 as its only solution
The equation has no real solutions.
The equation has x = 6 and x = -6 as its only solutions
The equation has an infinite number of solutions.
41. Which statement about the quadratic equation is true?
−6.5𝑥 2 + 416 = 0
E.
F.
G.
H.
The equation has a x=8 as its only solution
The equation has no real solutions.
The equation has x = 8 and x = -8 as its only solutions
The equation has an infinite number of solutions.
42. Solve the quadratic by factoring: 𝑥 2 − 8𝑥 + 12 = 0.
43. Solve the quadratic by factoring: 3𝑥 2 + 24𝑥 + 45 = 0.
44. Solve and give the answer in interval notation: 𝑥 2 − 10𝑥 + 24 > 0.
45. Solve and give the answer in interval notation: 𝑥 2 − 12𝑥 + 35 > 0.
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46. The graph of the quadratic function 𝑓 is shown on the grid below. What does the
solution set for 𝑓(𝑥) = 0 appear to be?
A.
B.
C.
D.
47. The graph of the quadratic function 𝑓 is shown on the grid below. What does the
solution set for 𝑓(𝑥) = 0 appear to be?
A.
B.
C.
D.