Question

Which statement regarding the function y=sin(x) is true?

Answer 1

Answer:

c. Reflection over either the x-axis or y-axis will change the graph

Step-by-step explanation:

a. Reflection over the y-axis will not change the graph since sine is an even function.

This is false because $y=sin(x)$ is an odd function, not an even one. This means that $sin(-x)=-sin(x)$, and a reflection over the y-axis will change the graph.

b. Sin(x)=sin(-x)

This is false because we said that $sin(-x)=-sin(x)$

c. Reflection over either the x-axis or y-axis will change the graph

This is true. Since $sin(x)$ 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 $f(x)$:

REFLEXION IN THE X-AXIS:

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

REFLEXION IN THE Y-AXIS:

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

d. Sin(x)=-sin(x)

False by the same explanation as b.