Question

The equations below represent transformations of the linear function y = -40x - 2. Match each equation with the corresponding change in the graph of y = -40x - 2

Answer 1

You have the following equation of a line:

`y=-40x-2`

You have to determine which transformation changes the previous equation into the following equations.

y = -10x - 2

You can notice that only the slope of the line has changed. In this case the transformation of the function is:

y(1/4 x) = -40(1/4x) - 2 = -10x - 2

that is, the transformation is a vertical compression by a factor of 1/4 about the line y = -2.

y = -20x - 2

You can notice that again the slope of the line has changed. The transformation is:

y(1/2 x) = -40(1/2x) - 2 = -20x - 2

that is, the transformation is a vertical compression by a factor of 1/2 about the line y = -

y = -60x - 2

The transformation is a vertical strech by a factor of 1.5 about the line y = -2.

In fact, you have:

y(1.5x) = -40(1.5x) - 2 = - 60x - 2

y = -80x - 2

The transformation is a vertical strech by a factor of 2 about the line y = -2.

In fact, you have

y(2x) = -40(2x) - 2 = -80x - 2