Q. 94 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that the graph of a function f is known. Explain how the graph of $y=4f\left(x\right)$ differs from the graph of $y=f\left(4x\right)$.

Step-by-Step Solution

Answer

For the function $y=4f\left(x\right)$, the function f  is stretched vertically $4$ units by  whereas for the function $y=f\left(4x\right)$ the function f  is compressed horizontally by $4$ units.

Step 1. Given Information

The given function is given as f.

Step 2. Difference between the graphs

We know that for function $y=af\left(x\right)$ the graph of function f  is stretched vertically if $a>1$ and for function $y=f\left(ax\right)$ the function f  is compressed horizontally if $a>1$.

Thus, for the function $y=4f\left(x\right)$ the function f  is stretched vertically by $4$ units whereas for the function $y=f\left(4x\right)$ the function f  is compressed horizontally by $4$ units.