5.7.1: Exercises
- Page ID
- 169544
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For the following exercises, evaluate the functions at the values \(f\left({-2}\right),f\left({-1}\right),f\left(0\right),f\left(1\right),\) and \(f\left(2\right)\).
\(f\left(x\right)=4-2x\)
\(f\left(x\right)=8-3x\)
\(f\left( x \right) = 8{x^2}-7x + 3\)
\(f\left( x \right) = 3 + \sqrt {x + 3} \)
\(f(x)=\frac{x-2}{x+3}\)
\(f(x)=x^3\)
For the following exercises, determine whether the ordered pairs represent a function.
\(\left\{ {\left( {-1,-1} \right),\left( {-2,-2} \right),\left( {-3,-3} \right)} \right\}\)
\(\left\{ {\left( {3,4} \right),\left( {4,5} \right),\left( {5,6} \right)} \right\}\)
\(\left\{ {\left( {2,5} \right),\left( {7,11} \right),\left( {15,8} \right),\left( {7,9} \right)} \right\}\)
\(\left\{ {\left( {-3{\text{ }},9} \right),\left( {-2,4} \right),\left( {-1,1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,4} \right),\left( {3,9} \right)} \right\}\)
\(\left\{ {\left( {9,-3} \right),\left( {4,-2} \right),\left( {1,-1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {4,{\text{ }}2} \right),\left( {9,3} \right)} \right\}\)
For the following exercises, determine whether the mapping represented a function.
For the following exercises, determine whether the equations represent \(y\) as a function of \(x\).
\(5x+2y=10\)
\(y = {x^2}\)
\(x = {y^2}\)
\(3{x^2} + y = 14\)
\(2x + {y^2} = 6\)
\(y = - 2{x^2} + 40x\)
For the following exercises, use the vertical line test to determine which graph represents a function.
For the following exercises, use the set of ordered pairs to find the domain and the range.
\(\left\{ {\left( {-3,9} \right),\left( {-2,4} \right),\left( {-1,1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,4} \right),\left( {3,9} \right)} \right\}\)
\(\left\{ {\left( {-9,-3} \right),\left( {-4,-2} \right),\left( {-1,-1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {4,2} \right),\left( {9,3} \right)} \right\}\)
\(\left\{ {\left( {-3,27} \right),\left( {-2,8} \right),\left( {-1,1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,8} \right),\left( {3,27} \right)} \right\}\)
\(\left\{ {\left( {-3,-27} \right),\left( {-2,-8} \right),\left( {-1,-1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,8} \right),\left( {3,27} \right)} \right\}\)
For the following exercises, use the graph to find the domain and the range.
