Question

How does the graph of f(x) = 5
cos 1/2 X

Answer 1

Answer:

The graph of $f(x)=5\cos(\frac{1}{2}x)$ is a vertical stretch of 5 units and a horizontal stretch by 2 units of the parent graph

Step-by-step explanation:

We want to find out how the graph of $f(x)=5\cos(\frac{1}{2}x)$ compare with the graph of the parent function $g(x)=\cos (x)$.

We can observe that the transformation applied to the basic cosine function is of the form:

$y=A \cos Bx$

The $A=5$ is a vertical stretch by a factor of 5 units.

$B=\frac{1}{2}$ is a horizontal stretch by a factor of 2 units.

Therefore the graph of $f(x)=5\cos(\frac{1}{2}x)$  will stretch vertically by a factor of 5 units and stretch horizontally by a factor of 2 units as compared to  $g(x)=\cos (x)$.

See attachment