What kind of transformation converts the graph of f(x)= – 4x–7 into the graph of g(x)= – 8x–7?

Question

The answer options are ...

horizontal stretch

horizontal shrink

vertical stretch

vertical shrink



Answer 1

What changed between the two equations? Well, the slope changed from a -4 to a -8. So which variable does that affect? The x or the y? The number multiplied by x affects the x-variable and the y-intercept affects the y-variable. Since the slope is multiplied by the x, we now know it affects the x-variable. The y-variable moves things up and down (that is, vertically) whereas the x-variable moves things left to right (that is, horizontally). So we have now narrowed our options down to horizontal stretch or horizontal shrink.

Now think about the slope. What makes the slope steeper or gradual? A steeper slope occurs when the number is greater than one and a gradual slope occurs when the slope is between zero and one. So which do we have here? We go from a steep line to steeper line. So you can think of it as stretching. It would be shrinking if we go from a steep line to a gradual line.