What this quiz covers
This quiz focuses on Read Inverses From Graphs Or Tables, giving you a quick way to practice the rules, question types, and explanations that matter most for Algebra 2.
Algebra 2 Quiz: Read Inverses From Graphs Or Tables
17 questions · exam conditions
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Read Inverses From Graphs Or TablesQuestion 1 of 17
The table gives outputs of a function f that has an inverse. Since points swap, (x,f(x)) on f corresponds to (f(x),x) on f−1. Use the table to find f−1(13).
| x | f(x) |
|---|---|
| 2 | 1 |
| 4 | 6 |
| 6 | 10 |
| 7 | 13 |
| 9 | 18 |
A7
B6
C13
D9
Algebra 2 Quiz
Algebra 2 Quiz: Read Inverses From Graphs Or Tables
Practice Read Inverses From Graphs Or Tables in Algebra 2 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
How to use this quiz
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
All questions
Question 1
The table gives outputs of a function f that has an inverse. Since points swap, (x,f(x)) on f corresponds to (f(x),x) on f−1. Use the table to find f−1(13).
| x | f(x) |
|---|---|
| 2 | 1 |
| 4 | 6 |
| 6 | 10 |
| 7 | 13 |
| 9 | 18 |
- 7 (correct answer)
- 6
- 13
- 9
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find f^{-1}(13), look in the f(x) column for the value 13; you'll see it's paired with x=7 in the table. Choice C correctly finds f⁻¹(13) = 7 by reading from the table properly. It's easy to misread and pick a nearby value like 6 or 9, but always verify the exact match in the output column— excellent work persisting through this! Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Example: table shows x: 1, 2, 3, 4 and f(x): 5, 9, 13, 17. To find f⁻¹(13), scan the f(x) column for 13 (found in row 3), read x from that row (x = 3), so f⁻¹(13) = 3. The swap happens automatically when you read this way!
Question 2
A one-to-one function f is shown by the table, so f has an inverse. Use the table to find f−1(12). (Look for the output 12 in the f(x) column; the corresponding x is the inverse value.)
| x | f(x) |
|---|---|
| 0 | 1 |
| 3 | 6 |
| 5 | 10 |
| 6 | 12 |
| 8 | 16 |
- f−1(12)=12
- f−1(12)=5
- f−1(12)=6 (correct answer)
- f−1(12)=8
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. Looking for f⁻¹(12), I scan the f(x) column for the value 12: f(0) = 1, f(3) = 6, f(5) = 10, f(6) = 12, f(8) = 16. Found it! When x = 6, f(x) = 12. Therefore, f⁻¹(12) = 6. Choice C correctly finds f⁻¹(12) = 6 by locating the row where f(x) = 12 and reading the corresponding x-value. Choice A incorrectly assumes f⁻¹(12) = 12, which would require f(12) = 12, but 12 isn't even an input in the table. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). The process naturally reverses the function's action!
Question 3
A one-to-one function f is shown by the table, so f has an inverse. Use the table to evaluate f−1(21). (Because inverse pairs swap, if f(x)=21 then f−1(21)=x.)
| x | f(x) |
|---|---|
| 2 | 9 |
| 4 | 13 |
| 6 | 17 |
| 8 | 21 |
| 10 | 25 |
- f−1(21)=8 (correct answer)
- f−1(21)=6
- f−1(21)=10
- f−1(21)=21
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To evaluate f⁻¹(21), I scan the f(x) column for 21: f(2) = 9, f(4) = 13, f(6) = 17, f(8) = 21, f(10) = 25. Found it! When x = 8, f(x) = 21. Therefore, f⁻¹(21) = 8. Choice C correctly finds f⁻¹(21) = 8 by locating where f(x) = 21 in the table. Choice A incorrectly assumes f⁻¹(21) = 21, which would require f(21) = 21, but 21 isn't even an input value in the table. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). The swap happens automatically when you read this way!
Question 4
Functions s and t are inverses of each other. If s(3)=7 and s(5)=2, what is the value of t(7)−t(2)?
- −2 (correct answer)
- 2
- 5
- 9
Explanation: Since s and t are inverses, t=s−1. From s(3)=7, we get t(7)=s−1(7)=3. From s(5)=2, we get t(2)=s−1(2)=5. Therefore, t(7)−t(2)=3−5=−2. Choice B gives ∣t(7)−t(2)∣. Choice C gives t(2)−t(7). Choice D gives t(7)+t(2)+3.
Question 5
Function k has an inverse, and the following values are known: k(1)=3, k(4)=−2, and k(7)=0. What is k−1(−2)+k−1(0)?
- 11 (correct answer)
- −2
- 3
- 5
Explanation: From k(4)=−2, we get k−1(−2)=4. From k(7)=0, we get k−1(0)=7. Therefore, k−1(−2)+k−1(0)=4+7=11. Choice B results from adding the output values −2+0. Choice C results from using k(1)=3 incorrectly. Choice D results from computing k−1(−2)+k−1(3)=4+1.
Question 6
The table gives values of a one-to-one function f, so f has an inverse. Use the table to find f−1(−4). (If (a,b) is on f, then (b,a) is on f−1.)
| x | f(x) |
|---|---|
| -3 | 5 |
| -1 | 1 |
| 0 | -2 |
| 2 | -4 |
| 4 | -7 |
- f−1(−4)=2 (correct answer)
- f−1(−4)=−4
- f−1(−4)=0
- f−1(−4)=4
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find f⁻¹(-4), I need to locate -4 in the f(x) column. Scanning down: f(-3) = 5, f(-1) = 1, f(0) = -2, f(2) = -4, f(4) = -7. I found it! When x = 2, f(x) = -4. Therefore, f⁻¹(-4) = 2. Choice A correctly finds f⁻¹(-4) = 2 by identifying that f(2) = -4 in the table. Choice B incorrectly assumes f⁻¹(-4) = -4, missing the fundamental swap property of inverses. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Remember: you're working backwards from output to input!
Question 7
A one-to-one function f is given by the table, so f has an inverse. What is f−1(14)?
| x | f(x) |
|---|---|
| 1 | −2 |
| 2 | 4 |
| 3 | 9 |
| 4 | 14 |
| 5 | 20 |
- f−1(14)=14
- f−1(14)=20
- f−1(14)=5
- f−1(14)=4 (correct answer)
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. Looking for f⁻¹(14), I scan the f(x) column and find f(4) = 14. This means when x = 4, the output is 14, so f⁻¹(14) = 4. Choice B correctly finds f⁻¹(14) = 4 by reading from the table that f(4) = 14 and applying the swap principle. Choice D incorrectly reads 20 from the table, which is actually f(5), not related to finding f⁻¹(14). Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Remember, you're working backwards—from output to input—which is exactly what an inverse function does!
Question 8
The table gives values of a one-to-one function f, so f has an inverse. Because inverse functions swap inputs and outputs, (a,b) on f corresponds to (b,a) on f−1. Use the table to determine f−1(−2).
- f−1(−2)=0
- f−1(−2)=−2
- f−1(−2)=2
- f−1(−2)=−1
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! The inverse reverses the input-output relationship. To find f⁻¹(-2), I need to locate -2 in the f(x) column and read the corresponding x-value. Looking at the table, when x = 0, f(x) = -2. Therefore, f⁻¹(-2) = 0. Choice A correctly finds f⁻¹(-2) = 0 by identifying that f(0) = -2 in the table. Choice B incorrectly suggests f⁻¹(-2) = -2, which is the common mistake of thinking a function's inverse at a point equals that point—but this would only be true if the point lies on the line y = x. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). In this case, -2 appears in the f(x) column when x = 0, so f⁻¹(-2) = 0.
Question 9
The table gives values of a one-to-one function f, so f has an inverse. Use the table to determine f−1(−4).
- f−1(−4)=3
- f−1(−4)=−4
- f−1(−4)=5
- f−1(−4)=8
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find f⁻¹(-4), I scan the f(x) column for -4. I see that f(3) = -4, which means when x = 3, the output is -4. Therefore, f⁻¹(-4) = 3. Choice A correctly finds f⁻¹(-4) = 3 by recognizing that since f(3) = -4, the inverse must map -4 back to 3. Choice B incorrectly assumes f⁻¹(-4) = -4, which would mean -4 is a fixed point, but the table shows f(-4) is not even defined. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a).
Question 10
The graph shows function r(x). Based on the graph, what is r−1(0)+r−1(2)?
- 1
- 2
- 4 (correct answer)
- 6
Explanation: To find r−1(0), locate where the graph has a y-value of 0, which occurs at x=−1. So r−1(0)=−1. To find r−1(2), locate where the graph has a y-value of 2, which occurs at x=5. So r−1(2)=5. Therefore, r−1(0)+r−1(2)=−1+5=4. Choice A results from adding the output values 0+2−1. Choice B results from counting intercepts incorrectly. Choice D results from using r−1(2)=4 instead of 5.
Question 11
Based on the table shown, what is the value of g−1(5)?
- −1
- 2
- 3 (correct answer)
- 8
Explanation: To find g−1(5), we need to find the input value that produces an output of 5. From the table, g(3)=5, so g−1(5)=3. Choice A gives g−1(−1) instead of g−1(5). Choice B gives g−1(8). Choice D gives g(5) instead of g−1(5).
Question 12
The table shows some values of function p(x). If p has an inverse, which of the following could be the value of p(6)?
- 1
- 3
- 5
- 9 (correct answer)
Explanation: For p to have an inverse, each output value must correspond to exactly one input value. The table shows outputs 1, 3, and 5 are already used, so p(6) cannot equal any of these values. Only 9 is not already an output value in the table. Choices A, B, and C would create repeated output values, violating the requirement for an inverse function.
Question 13
From the graph shown, if f−1(1)=−2, what is the value of f(−2)⋅f−1(−1)?
- −3
- 2
- 3 (correct answer)
- 6
Explanation: Given f−1(1)=−2, we know f(−2)=1. From the graph, we can read that f(3)=−1, so f−1(−1)=3. Therefore, f(−2)⋅f−1(−1)=1⋅3=3. Choice A results from using f−1(−1)=−3. Choice B results from computing f−1(1)+f(0)=−2+4. Choice D results from using f(−2)=−2 instead of 1.
Question 14
The graph shows function h(x). If h−1(4)=2, which point must be on the graph of h(x)?
- (2,4) (correct answer)
- (4,2)
- (−2,4)
- (2,−4)
Explanation: If h−1(4)=2, then by definition of inverse functions, h(2)=4. This means the point (2,4) is on the graph of h(x). Choice B confuses the roles of input and output. Choice C uses the wrong sign for the x-coordinate. Choice D uses the wrong sign for the y-coordinate.
Question 15
The function f is one-to-one, so it has an inverse. A point on the graph of f is (7,−3). Using the fact that (a,b) on f corresponds to (b,a) on f−1, what is f−1(−3)?
- f−1(−3)=−3
- f−1(−3)=7 (correct answer)
- f−1(−3)=3
- f−1(−3)=−7
Explanation: This question tests your ability to read values of an inverse function from given information using the fundamental property that inverses swap inputs and outputs. If f has a point (a, b), then f⁻¹ has the point (b, a)—every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(b), you look for the point on f where y = b and read the x-coordinate. Given that (7, -3) is on the graph of f, this means f(7) = -3. By the inverse relationship, this tells us that f⁻¹(-3) = 7. The coordinates swap! Choice B correctly identifies f⁻¹(-3) = 7 by recognizing that the point (7, -3) on f becomes the point (-3, 7) on f⁻¹. Choice A incorrectly suggests f⁻¹(-3) = -3, which would require the point (-3, -3) to be on f. Remember: the inverse function reverses the input-output relationship. If f takes 7 to -3, then f⁻¹ takes -3 back to 7. This swapping property is fundamental to understanding inverse functions!
Question 16
The function f is one-to-one and has an inverse. Use the table to find f−1(0).
| x | f(x) |
|---|---|
| −3 | −5 |
| −1 | −2 |
| 2 | 0 |
| 4 | 3 |
| 7 | 8 |
- 2 (correct answer)
- 4
- 0
- −2
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find f^{-1}(0), look in the f(x) column for the value 0; you'll see it's paired with x=2 in the table. Choice B correctly finds f⁻¹(0) = 2 by reading from the table properly. One might accidentally pick 0 or a negative, but recall we're reversing: find input for that output— you're making fantastic progress! Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Example: table shows x: 1, 2, 3, 4 and f(x): 5, 9, 13, 17. To find f⁻¹(13), scan the f(x) column for 13 (found in row 3), read x from that row (x = 3), so f⁻¹(13) = 3. The swap happens automatically when you read this way!
Question 17
The function f is one-to-one, so it has an inverse. Using the table, find f−1(2).
| x | f(x) |
|---|---|
| −2 | −4 |
| 0 | −1 |
| 1 | 2 |
| 3 | 5 |
| 6 | 9 |
- 1 (correct answer)
- −1
- 2
- 5
Explanation: This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find f^{-1}(2), look in the f(x) column for the value 2; you'll see it's paired with x=1 in the table. Choice C correctly finds f⁻¹(2) = 1 by reading from the table properly. Some students might mistakenly pick 2 itself or confuse with another row, but always focus on locating the output first and grabbing the input— you're doing great, keep going! Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Example: table shows x: 1, 2, 3, 4 and f(x): 5, 9, 13, 17. To find f⁻¹(13), scan the f(x) column for 13 (found in row 3), read x from that row (x = 3), so f⁻¹(13) = 3. The swap happens automatically when you read this way!