Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
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Question

Quizplus · Accepted Answer

The equation represents a function, meaning that for each input, there is only one output. Therefore, the inverse of the function can be graphed by switching the x and y coordinates of each point on the original graph. Option A does not include a solid line, Option C does not pass the vertical line test, and Option D does not correctly switch the x and y coordinates. Option B accurately graphs the function with a solid line and its inverse with a dashed line. The given graph represents a linear function, so its inverse will also be a linear function. To find the inverse, we can switch the x and y values and solve for y.

The equation of the given relation is y = 2x + 1. To find the inverse, we switch x and y:

x = 2y + 1

Solving for y:

x - 1 = 2y

y = (x - 1)/2

Therefore, the inverse of the relation is y = (x-1)/2.

To graph the inverse, we use a dashed line. The correct graph with the solid line representing the original function and the dashed line representing its inverse is shown in choice B.

Graph the Equation of the Relation Using a Solid Line