Chapter 1

Use the given function \(f\) to find and simplify the following: \- \(f(3)\) \- \(f(4 x)\) \- \(f(x-4)\) \- \(f(-1)\) \- \(4 f(x)\) -\(f(x)-4\) \- \(f\left(\frac{3}{2}\right)\) \- \(f(-x)\) \- \(f\left(x^{2}\right)\) $$f(x)=6$$

Graph the given relation. $$ \\{(x, y) \mid y<4\\} $$

Write the set using interval notation. $$ \\{x \mid x \leq 5 \text { or } x=6\\} $$

Suppose (2,-3) is on the graph of \(y=f(x) .\) In Exercises \(1-18,\) use Theorem 1.7 to find a point on the graph of the given transformed function. $$ y=\frac{4-f(3 x-1)}{7} $$

In Exercises \(13-20\), sketch the graph of the given piecewise-defined function. $$ f(x)=\left\\{\begin{array}{lll} \sqrt{x+4} & \text { if } & -4 \leq x<5 \\ \sqrt{x-1} & \text { if } & x \geq 5 \end{array}\right. $$

In Exercises \(11-20\), use the pair of functions \(f\) and \(g\) to find the domain of the indicated function then find and simplify an expression for it. $$ f(x)=x-1 \text { and } g(x)=\frac{1}{x-1} $$

Use the given function \(f\) to find and simplify the following: \- \(f(3)\) \- \(f(4 x)\) \- \(f(x-4)\) \- \(f(-1)\) \- \(4 f(x)\) -\(f(x)-4\) \- \(f\left(\frac{3}{2}\right)\) \- \(f(-x)\) \- \(f\left(x^{2}\right)\) $$f(x)=0$$

Graph the given relation. $$ \\{(x, y) \mid x \leq 3, y<2\\} $$

Write the set using interval notation. $$ \\{x \mid x>2 \text { or } x=\pm 1\\} $$

In Exercises \(13-20\), sketch the graph of the given piecewise-defined function. $$ f(x)=\left\\{\begin{array}{rll} x^{2} & \text { if } & x \leq-2 \\ 3-x & \text { if } & -2

In Exercises \(11-20\), use the pair of functions \(f\) and \(g\) to find the domain of the indicated function then find and simplify an expression for it. $$ f(x)=x \text { and } g(x)=\sqrt{x+1} $$

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$f(x)=2 x-5$$

Graph the given relation. $$ \\{(x, y) \mid x>0, y<4\\} $$

Write the set using interval notation. $$ \\{x \mid-3

In Exercises \(13-20\), sketch the graph of the given piecewise-defined function. $$ f(x)=\left\\{\begin{aligned} \frac{1}{x} & \text { if } \quad-6

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$f(x)=5-2 x$$

Graph the given relation. $$ \left\\{(x, y) \mid-\sqrt{2} \leq x \leq \frac{2}{3}, \pi

Plot and label the points \(A(-3,-7), B(1.3,-2), C(\pi, \sqrt{10}), D(0,8), E(-5.5,0), F(-8,4),\) \(G(9.2,-7.8)\) and \(H(7,5)\) in the Cartesian Coordinate Plane given below.

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=7 x $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=2 x-5 $$

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$f(x)=2 x^{2}-1$$

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=7 x+2 $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=-3 x+5 $$

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$f(x)=3 x^{2}+3 x-2$$

Find the distance \(d\) between the points and the midpoint \(M\) of the line segment which connects them. $$ (1,2),(-3,5) $$

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=7 $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=6 $$

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$f(x)=\sqrt{2 x+1}$$

Find the distance \(d\) between the points and the midpoint \(M\) of the line segment which connects them. $$ (3,-10),(-1,2) $$

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=3 x^{2}-4 $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=3 x^{2}-x $$

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$ f(x)=117 $$

Find the distance \(d\) between the points and the midpoint \(M\) of the line segment which connects them. $$ \left(\frac{1}{2}, 4\right),\left(\frac{3}{2},-1\right) $$

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=4-x^{2} $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=-x^{2}+2 x-1 $$

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$f(x)=\frac{x}{2}$$

Find the distance \(d\) between the points and the midpoint \(M\) of the line segment which connects them. $$ \left(-\frac{2}{3}, \frac{3}{2}\right),\left(\frac{7}{3}, 2\right) $$

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=x^{2}-x-6 $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=4 x^{2} $$

Use the given function \(f\) to find and simplify the following: \- \(f(2)\) \- \(2 f(a)\) \- \(f\left(\frac{2}{a}\right)\) \- \(f(-2)\) \- \(f(a+2)\) -\(\frac{f(a)}{2}\) \- \(f(2 a)\) \- \(f(a)+f(2)\) \- \(f(a+h)\) $$f(x)=\frac{2}{x}$$

Find the distance \(d\) between the points and the midpoint \(M\) of the line segment which connects them. $$ \left(\frac{24}{5}, \frac{6}{5}\right),\left(-\frac{11}{5},-\frac{19}{5}\right) $$

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=2 x^{3}-x $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=x-x^{2} $$

Use the given function \(f\) to find \(f(0)\) and solve \(f(x)=0\) $$f(x)=2 x-1$$

Find the distance \(d\) between the points and the midpoint \(M\) of the line segment which connects them. $$ (\sqrt{2}, \sqrt{3}),(-\sqrt{8},-\sqrt{12}) $$

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=-x^{5}+2 x^{3}-x $$

In Exercises \(21-45,\) find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the given function. $$ f(x)=x^{3}+1 $$

Use the given function \(f\) to find \(f(0)\) and solve \(f(x)=0\) $$f(x)=3-\frac{2}{5} x$$

Find the distance \(d\) between the points and the midpoint \(M\) of the line segment which connects them. $$ (2 \sqrt{45}, \sqrt{12}),(\sqrt{20}, \sqrt{27}) $$.

In Exercises \(21-41,\) determine analytically if the following functions are even, odd or neither. $$ f(x)=x^{6}-x^{4}+x^{2}+9 $$