MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

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-axisThe y-axis acts as the line of symmetry for the given graph.A graph is said to be symmetric about the Β 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 [tex]f(x) = f(-x)[/tex]A function f is even if the graph of f is symmetric with respect to the y-axisOdd function:A function is said to be odd if [tex]-f(x) = f(-x)[/tex] 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.