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.

Question

Mathematics

Demarcus Key

12 October, 07:30

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.

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Answers (1)

Know the Answer?

Rodney Parsons · 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