Evaluate the piecewise function at the given values of the independent variable. $$ h(x)=\left\{\begin{array}{lll}\frac{x^{2}-4}{x-2} & ext { if } x
eq 2 \ 7 & ext { if } x=2\end{array} ight. $$ $$ \begin{array}{lll} ext { (a) } h(3) & ext { (b) } h(0) & ext { (c) } h(2)\end{array} $$ $$ \begin{array}{ll} ext { (a) } h(3)=5 & h(0)=\square\end{array} $$

Question

Evaluate the piecewise function at the given values of the independent variable. $$ h(x)=\left\{\begin{array}{lll}\frac{x^{2}-4}{x-2} & 	ext { if } x 
eq 2 \ 7 & 	ext { if } x=2\end{array}ight. $$ $$ \begin{array}{lll}	ext { (a) } h(3) & 	ext { (b) } h(0) & 	ext { (c) } h(2)\end{array} $$ $$ \begin{array}{ll}	ext { (a) } h(3)=5 & h(0)=\square\end{array} $$

UpStudy AI · Accepted Answer

**(a) Evaluate $$ h(3) $$:**  
Since $$ 3 \neq 2 $$, use the formula  
$$
h(3)=\frac{3^2 - 4}{3-2}.
$$  
Compute the numerator:  
$$
3^2 - 4 = 9 - 4 = 5.
$$  
Compute the denominator:  
$$
3 - 2 = 1.
$$  
Thus,  
$$
h(3)=\frac{5}{1}=5.
$$

**(b) Evaluate $$ h(0) $$:**  
Since $$ 0 \neq 2 $$, use the formula  
$$
h(0)=\frac{0^2 - 4}{0-2}.
$$  
Compute the numerator:  
$$
0^2 - 4 = 0 - 4 = -4.
$$  
Compute the denominator:  
$$
0 - 2 = -2.
$$  
Thus,  
$$
h(0)=\frac{-4}{-2}=2.
$$

**(c) Evaluate $$ h(2) $$:**  
Since $$ x = 2 $$, we use the defined value for $$ x = 2 $$, which is:  
$$
h(2)=7.
$$

The answers are:  
$$
\text{(a)}\ h(3)=5,\quad \text{(b)}\ h(0)=2,\quad \text{(c)}\ h(2)=7.
$$
$$ h(3) = 5 $$, $$ h(0) = 2 $$, $$ h(2) = 7 $$.

Evaluate the piecewise function at the given values of the independent variable.

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