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\begin{document}
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\textbf{---Homework 1---}

In exercises 3-4, use the given function to evaluate each expression at each of
the following inputs.

\textbf{1.1 \#3.}  $F(x) = \frac{2x}{x^2-25}$.
\textbf{(a)} $F(3)$
\textbf{(b)} $F(-5)$
\textbf{(c)} $F(0)$
\textbf{(d)} $F(-7)$

\textbf{1.1 \#4.}  $b(x) = \sqrt{64-x^2}$
\textbf{(a)} $b(0)$
\textbf{(b)} $b(3)$
\textbf{(c)} $b(10)$
\textbf{(d)} $b(\sqrt{15})$

In exercises 8-9, (a) determine the domain of the function and express it
in interval notation.  (b)  Find the zeroes of the function.

\textbf{1.1 \#8.}  $q(n) = -\sqrt{2n-4}$.

\textbf{1.1 \#9.}  $F(y) = \frac{3y-5}{y^2-y-6}$.

In exercises 13-14, use the given function to simplify the expression.

\textbf{1.1 \#13.}  $P(x) = x^2+3$.
\textbf{(a)} $P(t+4)$
\textbf{(b)} $P(t) + P(4)$
\textbf{(c)} $P(t)+4$
\textbf{(d)} $t+P(4)$

\textbf{1.1 \#14.}  $Q(x) = \frac{3}{2x}$.
\textbf{(a)} $Q(2n)$
\textbf{(b)} $2Q(n)$
\textbf{(c)} $Q(2)\cdot Q(n)$
\textbf{(d)} $Q(2) \cdot n$

In exercises 25-26, simplify
$$
	\frac{f(x+h)-f(x)}{h}
$$

\textbf{1.1 \#25.} $f(x) = 4x+13$

\textbf{1.1 \#26.} $f(x) = 5-3x$

\textbf{1.1 \#31.}  Given the function
$$
	M(x) = \left\{
	\begin{matrix}
		-\frac{2}3{}x & & x < -4 \\
		5 & & -4 \le x < 2 \\
		\sqrt{2x} & & x \ge 2 \\
	\end{matrix}
	\right.
$$
evaluate
\textbf{(a)} $M(-7)$
\textbf{(b)} $M(-1)$
\textbf{(c)} $M(2)$
\textbf{(d)} $M(18)$

\textbf{1.1 \#32.}  Given the function
$$
	n(x) = \left\{
	\begin{matrix}
		-\sqrt 2 & & x < -3 \\
		x+5 & & -3 \le x \le 3 \\
		x^2-4& & x > 3 \\
	\end{matrix}
	\right.
$$
evaluate
\textbf{(a)} $n(-4)$
\textbf{(b)} $n(-3)$
\textbf{(c)} $n(3)$
\textbf{(d)} $n(6)$

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\vspace*{0.2in}
\textbf{---Homework 1---}

In exercises 3-4, use the given function to evaluate each expression at each of
the following inputs.

\textbf{1.1 \#3.}  $F(x) = \frac{2x}{x^2-25}$.
\textbf{(a)} $F(3)$
\textbf{(b)} $F(-5)$
\textbf{(c)} $F(0)$
\textbf{(d)} $F(-7)$

\textbf{1.1 \#4.}  $b(x) = \sqrt{64-x^2}$
\textbf{(a)} $b(0)$
\textbf{(b)} $b(3)$
\textbf{(c)} $b(10)$
\textbf{(d)} $b(\sqrt{15})$

In exercises 8-9, (a) determine the domain of the function and express it
in interval notation.  (b)  Find the zeroes of the function.

\textbf{1.1 \#8.}  $q(n) = -\sqrt{2n-4}$.

\textbf{1.1 \#9.}  $F(y) = \frac{3y-5}{y^2-y-6}$.

In exercises 13-14, use the given function to simplify the expression.

\textbf{1.1 \#13.}  $P(x) = x^2+3$.
\textbf{(a)} $P(t+4)$
\textbf{(b)} $P(t) + P(4)$
\textbf{(c)} $P(t)+4$
\textbf{(d)} $t+P(4)$

\textbf{1.1 \#14.}  $Q(x) = \frac{3}{2x}$.
\textbf{(a)} $Q(2n)$
\textbf{(b)} $2Q(n)$
\textbf{(c)} $Q(2)\cdot Q(n)$
\textbf{(d)} $Q(2) \cdot n$

In exercises 25-26, simplify
$$
	\frac{f(x+h)-f(x)}{h}
$$

\textbf{1.1 \#25.} $f(x) = 4x+13$

\textbf{1.1 \#26.} $f(x) = 5-3x$

\textbf{1.1 \#31.}  Given the function
$$
	M(x) = \left\{
	\begin{matrix}
		-\frac{2}3{}x & & x < -4 \\
		5 & & -4 \le x < 2 \\
		\sqrt{2x} & & x \ge 2 \\
	\end{matrix}
	\right.
$$
evaluate
\textbf{(a)} $M(-7)$
\textbf{(b)} $M(-1)$
\textbf{(c)} $M(2)$
\textbf{(d)} $M(18)$

\textbf{1.1 \#32.}  Given the function
$$
	n(x) = \left\{
	\begin{matrix}
		-\sqrt 2 & & x < -3 \\
		x+5 & & -3 \le x \le 3 \\
		x^2-4& & x > 3 \\
	\end{matrix}
	\right.
$$
evaluate
\textbf{(a)} $n(-4)$
\textbf{(b)} $n(-3)$
\textbf{(c)} $n(3)$
\textbf{(d)} $n(6)$

\end{document}
