Question

select all of the even functions.\
h(x) = -3x² - 8\
b(x) = -5x⁴ + 2x²\
w(x) = -x⁸ + 4x² - 5\
s(x) = -9x⁶ + 5x⁴ + 2x²

Explanation:

Step1: Recall even function definition

A function $f(x)$ is even if $f(-x) = f(x)$ for all $x$ in its domain.

Step2: Test $h(x)=-3x^2-8$

$h(-x) = -3(-x)^2 -8 = -3x^2 -8 = h(x)$

Step3: Test $b(x)=-5x^4+2x^2$

$b(-x) = -5(-x)^4 + 2(-x)^2 = -5x^4 + 2x^2 = b(x)$

Step4: Test $w(x)=-x^8+4x^2-5$

$w(-x) = -(-x)^8 + 4(-x)^2 -5 = -x^8 + 4x^2 -5 = w(x)$

Step5: Test $s(x)=-9x^6+5x^4+2x^2$

$s(-x) = -9(-x)^6 + 5(-x)^4 + 2(-x)^2 = -9x^6 + 5x^4 + 2x^2 = s(x)$

Answer:

All listed functions are even:

• $h(x) = -3x^2 - 8$
• $b(x) = -5x^4 + 2x^2$
• $w(x) = -x^8 + 4x^2 - 5$
• $s(x) = -9x^6 + 5x^4 + 2x^2$