Question

Given the function h(x) =1/3 |x-6| +4, evaluate the function when x = - 3, - 2, and 0

H(-3) =
H(-2)=
H(0)=

Answer 1

|x| = x for x ≥ 0

examples:

|3| = 3; |0.56| = 0.56; |102| = 102

|x| = -x for x < 0

examples:

|-3| = -(-3) = 3; |-0.56| = -(-0.56) = 0.56; |-102| = 102

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Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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`h(x)=(1)/(3)|x-6|+4`

Put the values of x to the equation of the function h(x):

`x=-3\to h(-3)=(1)/(3)|-3-6|+4=(1)/(3)|-9|+4=(1)/(3)(9)+4=3+4=7\\\\x=-2\to h(-2)=(1)/(3)|-2-6|+4=(1)/(3)|-8|+4=(1)/(3)(8)+4=(8)/(3)+(12)/(3)=(20)/(3)\\\\x=0\to h(0)=(1)/(3)|0-6|+4=(1)/(3)|-6|+4=(1)/(3)(6)+4=2+4=6`