Question

PLEASE HELP I AM SO CONFUSED

Answer 1

Answer:

9, 6 , 4

Step-by-step explanation:

(a)

h(3) with x = 3 ≠ 6 , use h(x) = $\frac{x^2-36}{x-6}$ , then

h(3) = $\frac{3^2-36}{3-6}$ = $\frac{9-36}{-3}$ = $\frac{-27}{-3}$ = 9

(b)

similarly h(0) with x = 0 ≠ 6 , then

h(0) = $\frac{0^2-36}{0-6}$ = $\frac{-36}{-6}$ = 6

(c)

h(6) with x = 6 then

h(6) = 4

Answer 2

Answer:

a)  h(3) = 9

b)  h(0) = 6

c)  h(6) = 4

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

$\sf h(x)=\begin{cases}\sf \dfrac{x^2-36}{x-6} &\textsf{if }x\neq 6\\\\\sf 4 & \textsf{if }x=6\end{cases}$

Therefore, the function has two definitions:

  $\sf h(x)=\dfrac{x^2-36}{x-6} \quad \textsf{when x does not equal 6}$

  $\sf h(x)=4 \quad \textsf{when x equals 6}$

Part (a)

h(3) means to substitute x = 3 into the function.

As x does not equal 6, substitute x = 3 into the first piece of the function:

$\begin{aligned}\sf \implies h(3) & =\sf \dfrac{(3)^2-36}{(3)-6}\\\\ & = \sf \dfrac{9-36}{-3}\\\\ & = \sf \dfrac{-27}{-3}\\\\ & = \sf 9\end{aligned}$

Part (b)

h(0) means to substitute x = 0 into the function.

As x does not equal 6, substitute x = 0 into the first piece of the function:

$\begin{aligned}\sf \implies h(0) & =\sf \dfrac{(0)^2-36}{(0)-6}\\\\ & = \sf \dfrac{0-36}{-6}\\\\ & = \sf \dfrac{-36}{-6}\\\\ & = \sf 6\end{aligned}$

Part (c)

h(6) means to substitute x = 6 into the function.

As x equals 6, then use the second piece of the function:

$\sf \implies h(6)=4$

Learn more about piecewise functions here:

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