Question

Determine whether the function shown in the graph is even or odd.

a. The function is even because it is symmetric with respect to the y-axis.
b. The function is odd because it is symmetric with respect to the y-axis.
c. The function is even because it is symmetric with respect to the origin.
d. The function is odd because it is symmetric with respect to the origin.

Answer 1

Answer:

Option A) The function is even because it is symmetric with respect to the y-axis.

Step-by-step explanation:

We are given a graph of the function.

We can see that the given function is symmetric around the y axis as the y axis acts as a mirror.

Symmetry around y-axis

• The y-axis acts as the line of symmetry for the given graph.

• A graph is said to be symmetric about the  y axis if (a,b) is on the graph, then we can find the point (-a,b) on the graph as well.

Even Function:

• A function is said to be even if

$f(x) = f(-x)$

• A function f is even if the graph of f is symmetric with respect to the y-axis

Odd function:

• A function is said to be odd if

$-f(x) = f(-x)$

• A function f is even if the graph of f is symmetric with respect to the x-axis.

Thus, we can write that the given function is an even function as the the graph is symmetric to the y-axis.

Option A) The function is even because it is symmetric with respect to the y-axis.