Question

Select the correct answer.

Which graph shows a function and its inverse?

A.
The graph shows two lines. The points on the green line are (minus 5, 4), (minus 3, 3), (minus 1, 2), (1, 1), and (3, 0). The points on the blue line are (minus 1, 5), (1, 1), and (2, minus 1). Both lines intersect at (1, 1).
B.
The graph shows two lines. The points on the green line are (minus 4, 4), (0, 3), and (4, 2). The points on the blue line are (minus 3, minus 5), (minus 1, 1), (minus 0.5, 3), and (0, 4). Both lines intersect at (minus 0.5, 3).
C.
The graph shows two lines. The points on the green line are (minus 2, 3), (minus 1, 0), and (0, minus 4). The points on the blue line are (minus 4, minus 2), (minus 1.1, minus 1.1), and (4, 0). Both lines intersect at (minus 1.1, minus 1.1).
D.
The graph shows two lines. The points on the green line are (minus 3, 5), (minus 1, 1), (0, minus 1), and (2, minus 5). The points on the blue line are (minus 1, minus 3), (0, minus 1), and (2, 3). Both lines intersect at (0, minus 1).

Answer 1

To determine which graph shows a function and its inverse, the points on the graph must reflect across the line y=x, showing symmetry.

Step-by-step explanation:

The question asks to identify which graph shows a function and its inverse. A function and its inverse have a unique relationship in which their coordinates are flipped in relation to the line y=x. This means if a function has a point (a, b), its inverse will have the point (b, a). When plotted on the same graph, a function and its inverse will be symmetrical along the line y=x.

Looking at the provided options, we need to find a pair of lines that show this symmetry. Without the specifics of the graph, we could determine which of the provided options might exhibit inverse characteristics, but to be precise, we must rely on the correct identification of the reflection property along the line y=x.

Moreover, understanding the concept of the slope is crucial. As stated in Figure A1 from the given reference material, the slope of a line is calculated by the rise over the run. In the context of identifying functions and their inverses, we should see a slope 'm' in the function and a slope '1/m' in its inverse if the function is linear. Given that none of the provided option details in the question provide enough information on their slopes, a definitive answer cannot be given without speculation.