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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.

Algebra 2

Read Inverses From Graphs Or Tables

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QUESTION
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Which value equals f−1(y)f^{-1}(y) if a table shows the pair (x,y)=(7,20)(x,y)=(7,20) for ff?

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ANSWER

f−1(20)=7f^{-1}(20)=7. The inverse reverses the input-output pair (7,20)(7,20).

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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.

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Flashcard 1: Which value equals f−1(y)f^{-1}(y) if a table shows the pair (x,y)=(7,20)(x,y)=(7,20) for ff?

Answer: f−1(20)=7f^{-1}(20)=7. The inverse reverses the input-output pair (7,20)(7,20).

Flashcard 2: What is f−1(3)f^{-1}(3) if the graph of ff includes (−1,3)( -1,3)?

Answer: f−1(3)=−1f^{-1}(3)=-1. Read the xx-coordinate where the graph has y=3y=3.

Flashcard 3: Identify the point on f−1f^{-1} that corresponds to the yy-intercept (0,c)(0,c) of ff.

Answer: The point (c,0)(c,0) on f−1f^{-1}. The yy-intercept of ff becomes the xx-intercept of f−1f^{-1}.

Flashcard 4: Identify f−1(0)f^{-1}(0) if a graph of ff crosses the yy-axis at (0,7)(0,7).

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

Flashcard 5: What is the yy-intercept of f−1f^{-1} if the xx-intercept of ff is (c,0)(c,0)?

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

Flashcard 6: What property must ff have (on its domain) to have an inverse function?

Answer: ff must be one-to-one. Each output must correspond to exactly one input.

Flashcard 7: What is the domain of f−1f^{-1} in terms of ff?

Answer: The domain of f−1f^{-1} is the range of ff. The inverse's inputs are the original function's outputs.

Flashcard 8: What is f^{-1}( rac{3}{2}) if the graph of ff includes (4, rac{3}{2})?

Answer: f^{-1}( rac{3}{2})=4. Read the xx-coordinate where the graph has y=32y=\frac{3}{2}.

Flashcard 9: What is f^{-1}(- rac{3}{4}) if a table shows f(2)=- rac{3}{4}?

Answer: f^{-1}(- rac{3}{4})=2. The inverse reverses the input-output pair (2,−34)(2,-\frac{3}{4}).

Flashcard 10: What is f−1(9)f^{-1}(9) if a graph of ff shows the point (1,9)(1,9)?

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

Flashcard 11: What is f−1(6)f^{-1}(6) if a graph of ff contains the point (4,6)(4,6)?

Answer: f−1(6)=4f^{-1}(6)=4. Read the xx-coordinate where the graph has y=6y=6.

Flashcard 12: What point lies on f−1f^{-1} if the point (−5,8)(-5,8) lies on ff?

Answer: (8,−5)(8,-5) lies on f−1f^{-1}. Inverse functions swap the coordinates of points.

Flashcard 13: Identify the range of ff if the domain of f−1f^{-1} is [−2,5][-2,5].

Answer: The range of ff is [−2,5][-2,5]. Domain and range swap between inverse functions.

Flashcard 14: What is f−1(1)f^{-1}(1) if the graph of ff includes ( rac{1}{2},1)?

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

Flashcard 15: What is f−1(a)f^{-1}(a) if f(4)=af(4)=a?

Answer: f−1(a)=4f^{-1}(a)=4. The inverse reverses any input-output relationship.

Flashcard 16: What happens to the domain and range when passing from ff to f−1f^{-1}?

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

Flashcard 17: What is f−1(5)f^{-1}(5) if a graph of ff has the point (−6,5)(-6,5)?

Answer: f−1(5)=−6f^{-1}(5)=-6. Read the xx-coordinate where the graph has y=5y=5.

Flashcard 18: What equation states the composition identity for inverses using f(f−1(x))f(f^{-1}(x))?

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

Flashcard 19: Which ordered pair on ff corresponds to the point (2,9)(2,9) on f−1f^{-1}?

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

Flashcard 20: Identify the meaning of the statement f−1(y)=xf^{-1}(y)=x in terms of ff.

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

Flashcard 21: What is the value of f−1(b)f^{-1}(b) if f(a)=bf(a)=b?

Answer: f−1(b)=af^{-1}(b)=a. Inverse functions reverse input-output relationships.

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

Answer: The point (0,c)(0,c) on f−1f^{-1}. The xx-intercept of ff becomes the yy-intercept of f−1f^{-1}.

Flashcard 23: What is f−1(x)f^{-1}(x) at x=−8x=-8 if the table shows f(0)=−8f(0)=-8?

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

Flashcard 24: What point lies on f−1f^{-1} if the point (0,−7)(0,-7) lies on ff?

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

Flashcard 25: What is f−1(12)f^{-1}(12) if a table shows f(9)=12f(9)=12?

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

Flashcard 26: Which ordered pair on f−1f^{-1} corresponds to the point (−3,11)(-3,11) on ff?

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

Flashcard 27: What is the value of f(a)f(a) if f−1(b)=af^{-1}(b)=a?

Answer: f(a)=bf(a)=b. If the inverse maps bb to aa, then ff maps aa to bb.

Flashcard 28: What is f−1(0)f^{-1}(0) if a table shows f(−4)=0f(-4)=0?

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

Flashcard 29: What is f^{-1}( rac{1}{2}) if a table shows f(8)= rac{1}{2}?

Answer: f^{-1}( rac{1}{2})=8. The inverse reverses the input-output pair (8,12)(8,\frac{1}{2}).

Flashcard 30: What is the range of f−1f^{-1} in terms of ff?

Answer: The range of f−1f^{-1} is the domain of ff. The inverse's outputs are the original function's inputs.

Flashcard 31: What is f−1(−6)f^{-1}(-6) if the graph of ff includes (2,−6)(2,-6)?

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

Flashcard 32: What equation states the composition identity for inverses using f−1(f(x))f^{-1}(f(x))?

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

Flashcard 33: What is f−1(−2)f^{-1}(-2) if the graph of ff includes (9,−2)(9,-2)?

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

Flashcard 34: What is the xx-intercept of f−1f^{-1} if the yy-intercept of ff is (0,c)(0,c)?

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

Flashcard 35: What is the key coordinate relationship between ff and f−1f^{-1} on a graph?

Answer: If (a,b)(a,b) is on ff, then (b,a)(b,a) is on f−1f^{-1}. Inverse functions swap xx and yy coordinates.

Flashcard 36: What is f−1(−3)f^{-1}(-3) if a table shows f(5)=−3f(5)=-3?

Answer: f−1(−3)=5f^{-1}(-3)=5. The inverse reverses the input-output pair (5,−3)(5,-3).

Flashcard 37: What is f−1(1)f^{-1}(1) if a table shows f(0)=1f(0)=1?

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

Flashcard 38: What point lies on f−1f^{-1} if the point (3,−2)(3,-2) lies on ff?

Answer: (−2,3)( -2,3) lies on f−1f^{-1}. Inverse functions swap the coordinates of points.

Flashcard 39: 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 40: What is f−1(b)f^{-1}(b) if f(−9)=bf(-9)=b?

Answer: f−1(b)=−9f^{-1}(b)=-9. The inverse reverses any input-output relationship.

Flashcard 41: What is f−1(x)f^{-1}(x) at x=4x=4 if the table shows f(1)=4f(1)=4?

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

Flashcard 42: Identify f−1(0)f^{-1}(0) if a graph of ff crosses the xx-axis at (7,0)(7,0).

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

Flashcard 43: What is f−1(2)f^{-1}(2) if a table shows f(−1)=2f(-1)=2?

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

Flashcard 44: What is f−1(10)f^{-1}(10) if a table shows f(3)=10f(3)=10?

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

Flashcard 45: What is f−1(13)f^{-1}(13) if the graph of ff includes (0,13)(0,13)?

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

Flashcard 46: What line reflects the graph of y=f(x)y=f(x) onto the graph of y=f−1(x)y=f^{-1}(x)?

Answer: The line y=xy=x. Functions and their inverses are reflections across this diagonal.

Flashcard 47: What is the value of f−1(b)f^{-1}(b) if the graph shows the point (b,a)(b,a) on f−1f^{-1}?

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

Flashcard 48: What is f−1(7)f^{-1}(7) if a table shows f(2)=7f(2)=7?

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

Flashcard 49: What is f−1(4)f^{-1}(4) if a graph of ff shows f(−2)=4f(-2)=4?

Answer: f−1(4)=−2f^{-1}(4)=-2. Find the input that produces output 44.

Flashcard 50: What is f−1(−1)f^{-1}(-1) if a graph of ff shows f(6)=−1f(6)=-1?

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

Flashcard 51: Which value equals f−1(y)f^{-1}(y) if a table shows the pair (x,y)=(−2,−9)(x,y)=(-2,-9) for ff?

Answer: f−1(−9)=−2f^{-1}(-9)=-2. The inverse reverses the input-output pair (−2,−9)(-2,-9).

Flashcard 52: What is the value of f(a)f(a) if the graph shows the point (a,b)(a,b) on ff?

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

Flashcard 53: Identify the domain of ff if the range of f−1f^{-1} is (0,10)(0,10).

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