Q:

Use the graph to answer the question.A line with a slope of negative 5 passing through the origin.see attached graphIs the function even, odd, or neither? Why? Select one belowThe function is even because it is symmetric about the y-axis.The function is odd because it is symmetric about the y-axis.The function is even because it is symmetric about the origin.The function is neither even nor odd because it is not symmetric about the y-axis or the origin.The function is odd because it is symmetric about the origin.

Accepted Solution

A:
Answer:The function is odd because it is symmetric about the origin.Step-by-step explanation:we know thatA function f(x) is even whenf(x)=f(-x) ----> the function is symmetry about the y-axisA function is odd when -f(x)=f(-x) ---> the function is symmetry about the originIn this problem we havef(x)=-5xVerify if the function is evenFor x=1 ----> f(1)=-5(1)=-5For x=-1 ---> f(-1)=-5(-1)=5sof(x) is not equal to f(-x)therefore The function is not evenVerify if the function is oddwe havef(1)=-5f(-1)=5so-f(1) is equal to f(-1)-f(x)=f(-x)thereforeThe function is odd because it is symmetric about the origin.