Question

In two or more complete sentences describe how to determine if the function, f(x)=3cos(x) is even by looking at a graph

Answer 1

A function is said to be even if its graph is symmetric with respect to the $y-axis$, that is:

$A \ function \ y=f(x) \ is \ \mathbf{even} \ if, \ for \ each \ x \ in \ the \ domain \ of \ f:\\ \\ f(-x)=f(x)$

Therefore:

SENTENCE 1:

<h3 />

• Since $f(x)=3cos(x)$ is symmetric with respect to the $y-axis$, then the function is even as illustrated in the Figure below.

SENTENCE 2:

• Since $f(x)=3cos(x) \ and \ f(-x)=3cos(-x)=3cos(x)$, thus $f(x)=f(-x)$, then the function is even as illustrated in the Figure below.