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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).

User Randakar
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2 Answers

2 votes

Answer:

A

Explanation:

User Martin Godzina
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6.3k points
4 votes

Answer:

A -- the curves that are not parabolas

Explanation:

The inverse relation will only be a function if it passes the vertical line test: a vertical line cannot intersect the curve at more than one point.

A "half-parabola" can have an inverse function.

A parabola will have an inverse relation that is not a function. When x-values are repeated, as "goes through (5, 2) and goes through (5, -2)", the relation is not a function.

The graph that shows inverse functions is attached. A function and its inverse are mirror images of each other in the line y=x.

Which graph shows a function whose inverse is also a function? On a coordinate plane-example-1
User Josh Reich
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7.4k points
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