Question

Part 1.] Identify the transformations that describe the graph of an odd function. Select all that apply.

reflection over the x-axis;
reflection over the y-axis;
reflection over the line y = x;
90° rotation around the origin;
180° rotation around the origin

Part 2.] Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.

Answer 1

Hello,

1) A odd function has the propriety f(-x)=-f(x)
Answer E

2)
if f(x) is even f(x)=f(-x)
if g(x) is even g(x)=g(-x)

h(x)=f(x)+g(x)=(f+g)(x)
h(-x)=(f+g)(-x)=f(-x)+g(-x)=f(x)+g(x)=(f+g)(x)=h(x)

h(x) is even