Question

Part C: The graph y = P(x) is shown.

What property of an even function do you see in this graph?

Part D
An equation for y = P(x) is shown.

Part C: The graph y = P(x) is shown.
20
-16
What property of an even function do you see in this graph?
Part D
An equation for y = P(x) is shown. y=P(x)=x+ - 8x² + 16
State the algebraic definition of an even function. Show algebraically that P(x) is an even
function for all values of x.

function for all values of x.

Answer 1

C. The property seen in the graph is symmetry on the y-axis

D. The even function is defined by f(x) = f(-x)

How to show that the function is an even function

An even function is a function f(x) that satisfies the property

• f(x) = f(-x)

This means that if you replace x with -x in the function, you get the same output

Check

P(x) = x⁴ - 8x² + 16

P(-x) = (-x)⁴ - 8(-x)² + 16

P(-x) = x⁴ - 8x² + 16

Comparing with the original function shows that P(-x) = P(x). Hence the function is even.