Answers 2627 ALGEBRA II AFunction Operations

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Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?

The graph of f(x) passes the vertical line test.

f(x) is a one-to-one function.

The graph of the inverse of f(x) passes the horizontal line test.

f(x) is not a function.

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If and , which expression could be used to verify g(x) is the inverse of f(x)?

one-fifth (one-fifth x + 5) + 5

One-fifth (5 x minus 25) + 5

StartFraction 1 Over (one-fifth x + 5) EndFraction

5 (one-fifth x + 5) + 5

Which graph shows a function whose inverse is also a function?

On a coordinate plane, 2 curves are shown. f (x) is a curve that starts at (0, 0) and opens down and to the right in quadrant 1. The curve goes through (4, 2). The inverse of f (x) starts at (0, 0) and curves up sharply and opens to the left in quadrant 1. The curve goes through (2, 4).

On a coordinate plane, 2 parabolas are shown. f (x) opens up and goes through (negative 2, 5), has a vertex at (0, negative 2), and goes through (2, 5). The inverse of f (x) opens right and goes through (5, 2), has a vertex at (negative 2, 0), and goes through (5, negative 2).

On a coordinate plane, two v-shaped graphs are shown. f (x) opens down and goes through (0, negative 3), has a vertex at (1, 3), and goes through (2, negative 3). The inverse of f (x) opens to the left and goes through (negative 3, 2), has a vertex at (3, 1), and goes through (negative 3, 0).

On a coordinate plane, two curved graphs are shown. f (x) sharply increases from (negative 1, negative 4) to (0, 2) and then changes directions and curves down to (1, 1). At (1, 1) the curve changes directions and curves sharply upwards. The inverse of f (x) goes through (negative 4, negative 1) and gradually curves up to (2, 0). At (2, 0) the curve changes directions sharply and goes toward (1, 1). At (1, 1), the curve again sharply changes directions and goes toward (3, 1).

The function h(x) is given below.h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}Which of the following gives h–1(x)?

{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}

{(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}

{(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}

{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)}

Which function has an inverse that is also a function?

{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)}

{(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)}

{(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)}

{(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

If and , which expression could be used to verify that is the inverse of ?

one-third (one-third x)

Option

The function f(x) is shown below.xf(x)–61–32255380If g(x) is the inverse of f(x), what is the value of f(g(2))?

–6

–3

Which function has an inverse that is also a function?

{(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)}

{(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)}

{(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

{(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).

On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).

On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).

On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).

If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

(0, –2)

(1, –1)

(2, 0)

(3, 3)

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