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  3. Algebra 2

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Algebra 2 Flashcards: Read Inverses From Graphs Or Tables

Study Read Inverses From Graphs Or Tables in Algebra 2 with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

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What this deck covers

This deck focuses on Read Inverses From Graphs Or Tables, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Algebra 2 Flashcards: Read Inverses From Graphs Or Tables

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QUESTION

What is f−1(13)f^{-1}(13)f−1(13) if the graph of fff includes (0,13)(0,13)(0,13)?

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ANSWER

f−1(13)=0f^{-1}(13)=0f−1(13)=0. Read the xxx-coordinate where the graph has y=13y=13y=13.

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Flashcard 1: What is f−1(13)f^{-1}(13)f−1(13) if the graph of fff includes (0,13)(0,13)(0,13)?

Answer: f−1(13)=0f^{-1}(13)=0f−1(13)=0. Read the xxx-coordinate where the graph has y=13y=13y=13.

Flashcard 2: What is f−1(−2)f^{-1}(-2)f−1(−2) if the graph of fff includes (9,−2)(9,-2)(9,−2)?

Answer: f−1(−2)=9f^{-1}(-2)=9f−1(−2)=9. Read the xxx-coordinate where the graph has y=−2y=-2y=−2.

Flashcard 3: What happens to the domain and range when passing from fff to f−1f^{-1}f−1?

Answer: Domain and range swap between fff and f−1f^{-1}f−1. The input set of one becomes the output set of the other.

Flashcard 4: What is f−1(7)f^{-1}(7)f−1(7) if a table shows f(2)=7f(2)=7f(2)=7?

Answer: f−1(7)=2f^{-1}(7)=2f−1(7)=2. The inverse reverses the input-output pair (2,7)(2,7)(2,7).

Flashcard 5: What equation states the composition identity for inverses using f−1(f(x))f^{-1}(f(x))f−1(f(x))?

Answer: f−1(f(x))=xf^{-1}(f(x))=xf−1(f(x))=x (for xxx in the domain of fff). Composing an inverse with its function yields the identity.

Flashcard 6: What graph test checks whether a function is one-to-one?

Answer: The horizontal line test. No horizontal line intersects the graph more than once.

Flashcard 7: Identify the meaning of the statement f−1(y)=xf^{-1}(y)=xf−1(y)=x in terms of fff.

Answer: It means f(x)=yf(x)=yf(x)=y. The inverse notation shows which input produces output yyy.

Flashcard 8: What is the yyy-intercept of f−1f^{-1}f−1 if the xxx-intercept of fff is (c,0)(c,0)(c,0)?

Answer: The yyy-intercept of f−1f^{-1}f−1 is (0,c)(0,c)(0,c). Intercepts swap coordinates when finding the inverse.

Flashcard 9: What is f−1(0)f^{-1}(0)f−1(0) if a table shows f(−4)=0f(-4)=0f(−4)=0?

Answer: f−1(0)=−4f^{-1}(0)=-4f−1(0)=−4. The inverse reverses the input-output pair (−4,0)(-4,0)(−4,0).

Flashcard 10: What is f−1(12)f^{-1}(12)f−1(12) if a table shows f(9)=12f(9)=12f(9)=12?

Answer: f−1(12)=9f^{-1}(12)=9f−1(12)=9. The inverse reverses the input-output pair (9,12)(9,12)(9,12).

Flashcard 11: What point lies on f−1f^{-1}f−1 if the point (0,−7)(0,-7)(0,−7) lies on fff?

Answer: (−7,0)(-7,0)(−7,0) lies on f−1f^{-1}f−1. Inverse functions swap the coordinates of points.

Flashcard 12: What is f−1(2)f^{-1}(2)f−1(2) if a table shows f(−1)=2f(-1)=2f(−1)=2?

Answer: f−1(2)=−1f^{-1}(2)=-1f−1(2)=−1. The inverse reverses the input-output pair (−1,2)(-1,2)(−1,2).

Flashcard 13: What is f−1(10)f^{-1}(10)f−1(10) if a table shows f(3)=10f(3)=10f(3)=10?

Answer: f−1(10)=3f^{-1}(10)=3f−1(10)=3. The inverse reverses the input-output pair (3,10)(3,10)(3,10).

Flashcard 14: Identify f−1(0)f^{-1}(0)f−1(0) if a graph of fff crosses the xxx-axis at (7,0)(7,0)(7,0).

Answer: f−1(0)=7f^{-1}(0)=7f−1(0)=7. The xxx-intercept shows where f(x)=0f(x)=0f(x)=0.

Flashcard 15: Identify f−1(0)f^{-1}(0)f−1(0) if a graph of fff crosses the yyy-axis at (0,7)(0,7)(0,7).

Answer: f−1(0)f^{-1}(0)f−1(0) is not determined from (0,7)(0,7)(0,7) alone. The yyy-intercept alone doesn't show where f(x)=0f(x)=0f(x)=0.

Flashcard 16: What is f−1(x)f^{-1}(x)f−1(x) at x=4x=4x=4 if the table shows f(1)=4f(1)=4f(1)=4?

Answer: f−1(4)=1f^{-1}(4)=1f−1(4)=1. The inverse reverses the input-output pair (1,4)(1,4)(1,4).

Flashcard 17: What is f−1(x)f^{-1}(x)f−1(x) at x=−8x=-8x=−8 if the table shows f(0)=−8f(0)=-8f(0)=−8?

Answer: f−1(−8)=0f^{-1}(-8)=0f−1(−8)=0. The inverse reverses the input-output pair (0,−8)(0,-8)(0,−8).

Flashcard 18: What is the value of f−1(b)f^{-1}(b)f−1(b) if the graph shows the point (b,a)(b,a)(b,a) on f−1f^{-1}f−1?

Answer: f−1(b)=af^{-1}(b)=af−1(b)=a. Reading coordinates directly from the inverse graph.

Flashcard 19: What is the value of f(a)f(a)f(a) if the graph shows the point (a,b)(a,b)(a,b) on fff?

Answer: f(a)=bf(a)=bf(a)=b. Reading coordinates directly from the function graph.

Flashcard 20: Which ordered pair on fff corresponds to the point (2,9)(2,9)(2,9) on f−1f^{-1}f−1?

Answer: (9,2)(9,2)(9,2) on fff. Inverse functions swap coordinates of corresponding points.

Flashcard 21: Which ordered pair on f−1f^{-1}f−1 corresponds to the point (−3,11)(-3,11)(−3,11) on fff?

Answer: (11,−3)(11,-3)(11,−3) on f−1f^{-1}f−1. Inverse functions swap coordinates of corresponding points.

Flashcard 22: Identify the point on f−1f^{-1}f−1 that corresponds to the yyy-intercept (0,c)(0,c)(0,c) of fff.

Answer: The point (c,0)(c,0)(c,0) on f−1f^{-1}f−1. The yyy-intercept of fff becomes the xxx-intercept of f−1f^{-1}f−1.

Flashcard 23: Identify the point on f−1f^{-1}f−1 that corresponds to the xxx-intercept (c,0)(c,0)(c,0) of fff.

Answer: The point (0,c)(0,c)(0,c) on f−1f^{-1}f−1. The xxx-intercept of fff becomes the yyy-intercept of f−1f^{-1}f−1.

Flashcard 24: What is f−1(−6)f^{-1}(-6)f−1(−6) if the graph of fff includes (2,−6)(2,-6)(2,−6)?

Answer: f−1(−6)=2f^{-1}(-6)=2f−1(−6)=2. Read the xxx-coordinate where the graph has y=−6y=-6y=−6.

Flashcard 25: What is f−1(1)f^{-1}(1)f−1(1) if the graph of fff includes ( rac{1}{2},1)?

Answer: f^{-1}(1)= rac{1}{2}. Read the xxx-coordinate where the graph has y=1y=1y=1.

Flashcard 26: What point lies on f−1f^{-1}f−1 if the point (0,−7)(0,-7)(0,−7) lies on fff?

Answer: (−7,0)(-7,0)(−7,0) lies on f−1f^{-1}f−1. Inverse functions swap the coordinates of points.

Flashcard 27: What is f−1(−1)f^{-1}(-1)f−1(−1) if a graph of fff shows f(6)=−1f(6)=-1f(6)=−1?

Answer: f−1(−1)=6f^{-1}(-1)=6f−1(−1)=6. Find the input that produces output −1-1−1.

Flashcard 28: Identify the domain of fff if the range of f−1f^{-1}f−1 is (0,10)(0,10)(0,10).

Answer: The domain of fff is (0,10)(0,10)(0,10). Domain and range swap between inverse functions.

Flashcard 29: What is f−1(7)f^{-1}(7)f−1(7) if a table shows f(2)=7f(2)=7f(2)=7?

Answer: f−1(7)=2f^{-1}(7)=2f−1(7)=2. The inverse reverses the input-output pair (2,7)(2,7)(2,7).

Flashcard 30: What is f−1(0)f^{-1}(0)f−1(0) if a table shows f(−4)=0f(-4)=0f(−4)=0?

Answer: f−1(0)=−4f^{-1}(0)=-4f−1(0)=−4. The inverse reverses the input-output pair (−4,0)(-4,0)(−4,0).