contestada

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 function
b. Sin(x)=sin(-x)
c. Reflection over either the x-axis or y-axis will change the graph
d. Sin(x)=-sin(x)

Respuesta :

danielmaduroh

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 [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 graph

This 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.