Question

How does the graph of f(x)=4 cos(1/2x)-3 differ from the graph of g(x)=4 cos(x)-3

Answer 1

Answer:

The function f(x) is stretched horizontally.

Step-by-step explanation:

We are asked to determine how the graph of $f(x)=4\text{cos}(\frac{1}{2}x)-3$ differ from the graph of $g(x)=4\text{cos}(x)-3$.

Let us recall transformation rules of functions.

$f(ax)\rightarrow$

If $a>1$ function compresses horizontally.

If $a$ function stretches horizontally.

Upon looking at function $f(x)=4\text{cos}(\frac{1}{2}x)-3$, we can see that the value of 'a' is less than 1 that is $\frac{1}{2}$, therefore, the function f(x) is stretched horizontally.

Answer 2

The graph of f(x)=4 cos(1/2x)-3 differs from the graph of g(x)=4 cos(x)-3, f(x) is stretched horizontally.