Respuesta :
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.
Answer:
The function f(x) is stretched horizontally.
Step-by-step explanation:
We are asked to determine how the graph of [tex]f(x)=4\text{cos}(\frac{1}{2}x)-3[/tex] differ from the graph of [tex]g(x)=4\text{cos}(x)-3[/tex].
Let us recall transformation rules of functions.
[tex]f(ax)\rightarrow[/tex]
If [tex]a>1[/tex] function compresses horizontally.
If [tex]a<1[/tex] function stretches horizontally.
Upon looking at function [tex]f(x)=4\text{cos}(\frac{1}{2}x)-3[/tex], we can see that the value of 'a' is less than 1 that is [tex]\frac{1}{2}<1[/tex], therefore, the function f(x) is stretched horizontally.
