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$f(x)=\left|x-5\right|$
$f(x)=\left|2x-4\right|$
For the following exercises, solve the absolute value equation.
$\left|\frac{1}{3}x+5\right|=\left|\frac{3}{4}x-2\right|$
For the following exercises, solve the inequality and express the solution using interval notation.
$\left|\frac{1}{3}x-2\right|\le 7$
For the following exercises, find $\text{}{f}^{-1}(x)\text{}$ for each function.
$f(x)=9+10x$
For the following exercise, find a domain on which the function $\text{}f\text{}$ is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of $\text{}f\text{}$ restricted to that domain.
$f(x)={x}^{2}+1$
Given $f\left(x\right)={x}^{3}-5$ and $g(x)=\sqrt[3]{x+5}:$
For the following exercises, use a graphing utility to determine whether each function is one-to-one.
If $f\left(1\right)=4,$ find ${f}^{-1}(4).$
For the following exercises, determine whether each of the following relations is a function.
$\left\{(2,1),(3,2),(-1,1),(0,-2)\right\}$
For the following exercises, evaluate the function $\text{\hspace{0.17em}}f(x)=-3{x}^{2}+2x\text{\hspace{0.17em}}$ at the given input.
$\text{\hspace{0.17em}}f(a)\text{\hspace{0.17em}}$
Show that the function $\text{\hspace{0.17em}}f(x)=-2{(x-1)}^{2}+3\text{\hspace{0.17em}}$ is not one-to-one.
The graph is a parabola and the graph fails the horizontal line test.
Write the domain of the function $\text{\hspace{0.17em}}f(x)=\sqrt{3-x}\text{\hspace{0.17em}}$ in interval notation.
Given $\text{\hspace{0.17em}}f(x)=2{x}^{2}-5x,\text{\hspace{0.17em}}$ find $\text{\hspace{0.17em}}f(a+1)-f(1).$
$2{a}^{2}-a$
Graph the function $f(x)=\{\begin{array}{cc}x+1\text{if}& -2x3\\ \text{}-x\text{if}& x\ge 3\end{array}$
Find the average rate of change of the function $\text{\hspace{0.17em}}f(x)=3-2{x}^{2}+x\text{\hspace{0.17em}}$ by finding $\text{\hspace{0.17em}}\frac{f(b)-f(a)}{b-a}.$
$-2(a+b)+1$
For the following exercises, use the functions $\text{\hspace{0.17em}}f(x)=3-2{x}^{2}+x\text{and}g(x)=\sqrt{x}\text{\hspace{0.17em}}$ to find the composite functions.
$\left(g\circ f\right)(x)$
Express $\text{\hspace{0.17em}}H(x)=\sqrt[3]{5{x}^{2}-3x}\text{\hspace{0.17em}}$ as a composition of two functions, $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}g,\text{\hspace{0.17em}}$ where $\text{\hspace{0.17em}}\left(f\circ g\right)(x)=H(x).$
For the following exercises, graph the functions by translating, stretching, and/or compressing a toolkit function.
$f(x)=\frac{1}{x+2}-1$
For the following exercises, determine whether the functions are even, odd, or neither.
$f(x)=-\frac{5}{{x}^{3}}+9{x}^{5}$
Graph the absolute value function $\text{\hspace{0.17em}}f(x)=-2\left|x-1\right|+3.$
Solve $\left|2x-3\right|=17.$
$x=-7\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}x=10$
Solve $\text{\hspace{0.17em}}-\left|\frac{1}{3}x-3\right|\ge 17.\text{\hspace{0.17em}}$ Express the solution in interval notation.
For the following exercises, find the inverse of the function.
$f(x)=\frac{4}{x+7}$
For the following exercises, use the graph of $\text{\hspace{0.17em}}g\text{\hspace{0.17em}}$ shown in [link] .
On what intervals is the function increasing?
$(-\infty ,-1.1)\text{and}(1.1,\infty )$
On what intervals is the function decreasing?
Approximate the local minimum of the function. Express the answer as an ordered pair.
$\left(1.1,-0.9\right)$
Approximate the local maximum of the function. Express the answer as an ordered pair.
For the following exercises, use the graph of the piecewise function shown in [link] .
Find $\text{\hspace{0.17em}}f(\mathrm{-2}).$
Write an equation for the piecewise function.
$f(x)=\{\begin{array}{c}\left|x\right|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x\le 2\\ 3\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x>2\end{array}$
For the following exercises, use the values listed in [link] .
$x$ | $F(x)$ |
0 | 1 |
1 | 3 |
2 | 5 |
3 | 7 |
4 | 9 |
5 | 11 |
6 | 13 |
7 | 15 |
8 | 17 |
Find $\text{\hspace{0.17em}}F(6).$
Is the graph increasing or decreasing on its domain?
Find $\text{\hspace{0.17em}}{F}^{-1}(15).$
Given $\text{\hspace{0.17em}}f(x)=-2x+11,\text{\hspace{0.17em}}$ find $\text{\hspace{0.17em}}{f}^{-1}(x).$
${f}^{-1}(x)=-\frac{x-11}{2}$
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