MATH SOLVE

2 months ago

Q:
# which statement regarding the function y=sin(x) is true?a. Reflection over the y-axis will not change the graph since sine is an even functionb. Sin(x)=sin(-x)c. Reflection over either the x-axis or y-axis will change the graphd. Sin(x)=-sin(x)

Accepted Solution

A:

Answer:c. Reflection over either the x-axis or y-axis will change the graphStep-by-step explanation:a. Reflection over the y-axis will not change the graph since sine is an even function.This is false because [tex]y=sin(x)[/tex] is an odd function, not an even one. This means that [tex]sin(-x)=-sin(x)[/tex], and a reflection over the y-axis will change the graph.b. Sin(x)=sin(-x)This is false because we said that [tex]sin(-x)=-sin(x)[/tex]c. Reflection over either the x-axis or y-axis will change the graphThis is true. Since [tex]sin(x)[/tex] is an odd function, then reflection over either the x-axis or y-axis will change the graph as we said in a. So, for [tex]f(x)[/tex]:REFLEXION IN THE X-AXIS:[tex]h(x)=-f(x)[/tex]REFLEXION IN THE Y-AXIS:[tex]h(x)=f(-x)[/tex]d. Sin(x)=-sin(x)False by the same explanation as b.