Unit 6 Test Review - Compositions and Inverses
Quiz
•
Mathematics
•
12th Grade
•
Medium
+4
Standards-aligned
Judith M Alvarado
Used 16+ times
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37 questions
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1.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
f(x) = 2x - 5
g(x) = -4x - 2
Find f(g(-2))
25
-25
-7
7
Answer explanation
First, calculate g(-2): g(-2) = -4(-2) - 2 = 8 - 2 = 6. Then, find f(6): f(6) = 2(6) - 5 = 12 - 5 = 7. Thus, f(g(-2)) = 7.
Tags
CCSS.HSF-BF.A.1C
2.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
If f(x) = 5x and g(x) = 2x-1,
what is the composition f(g(x)) ?
10x-1
10x-5
5x2-1
5x2-5
Answer explanation
To find f(g(x)), substitute g(x) into f(x): f(g(x)) = f(2x-1) = 5(2x-1) = 10x - 5. Thus, the correct answer is 10x-5.
Tags
CCSS.HSF-BF.A.1C
3.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
34
71
35
142
Answer explanation
First, calculate g(3): g(3) = 2(3^2) - 1 = 2(9) - 1 = 18 - 1 = 17. Then, find f(g(3)): f(17) = 2(17) = 34. Thus, the answer is 34.
Tags
CCSS.HSF-BF.A.1C
4.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Find the inverse: f(x) = 3x + 2
f-1(x) = 2x + 3
f-1(x) = -3x + 2
f-1(x) = (x-2)/3
f-1(x) = (x-3)/2
Answer explanation
To find the inverse of f(x) = 3x + 2, swap x and y: x = 3y + 2. Solve for y: y = (x - 2)/3. Thus, f-1(x) = (x - 2)/3, which is the correct choice.
Tags
CCSS.HSF-BF.B.4A
5.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
To graph the inverse of a function...
Rotate it around the origin
Reflect it across the x-axis
Reflect it across the y-axis
Switch the x and y coordinates and plot the new points
Answer explanation
To graph the inverse of a function, you switch the x and y coordinates of each point on the original graph. This reflects the graph across the line y=x, which is the correct method for finding the inverse.
Tags
CCSS.HSF-BF.B.4C
6.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Tags
CCSS.HSF-BF.B.4A
7.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
A function, f(x), goes through (1, 4) and (4, 6), what points below does it's inverse f-1(x) go through?
(1, 4) and (4, 6)
(-4, -1) and (-6, -4)
(-1, -4) and (-4, -6)
(4, 1) and (6, 4)
Answer explanation
The inverse function f-1(x) swaps the coordinates of the points on f(x). Therefore, the points (1, 4) and (4, 6) on f(x) correspond to (4, 1) and (6, 4) on f-1(x). Thus, the correct answer is (4, 1) and (6, 4).
Tags
CCSS.HSF-BF.B.4C
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