4.5: Chapter 4 Review
- Page ID
- 154458
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)PROBLEM SET: CHAPTER 4 REVIEW
Functions and Function Notation (4.1)
- Consider the set of points \({3,5), (5,4), (2,9), (0,5), (7,9)}\).
- Find the domain.
- Find the range.
- Do these points represent a function?
- For the function \(f(x)=-x^{2}-8\), evaluate each of the following.
- \(f(3)\)
- \(f(-3)\)
- For the function \(g(x)=-3x+4\), evaluate each of the following.
- \(g(2)\)
- \(g(x)+2\)
- \(g(x)+2\)
Understanding the Basic Functions (4.2)
- Without relying on technology, sketch a graph with at least 3 points of each of the following functions.
- \(f(x)=x^{3}\)
- \(f(x)=|x|\)
- \(f(x)=x\)
- \(f(x)=\sqrt{x}\)
- \(f(x)=c\)
- \(f(x)=\dfrac{1}{x}\)
- \(f(x)=x^{2}\)
- Given the function \(f (xt ) = \left\{ \begin{array} { l l } { 5x-7 } & { \text { if } x \leq -1 } \\ { -2x^{2} + 5 } & { \text { if } x > 0 } \end{array} \right.\), find each of the following values.
- \(f(-4)\)
- \(f(-1)\)
- \(f(3)\)
Transformations of Functions (4.3)
- For each function below, identify the basic function, describe the transformations, and sketch a graph of the transformed function.
- \(f(x)=\sqrt{x+9}\)
- \(g(x)=\dfrac{1}{x}-2\)
- \(h(x)=|x-4|+3\)
- \(j(x)=-x^{2}-8\)
- For each function shown below, identify the basic function, describe the transformations, and find an equation for the function.
-
Quadratic Functions and Their Applications (4.4)
- How can you determine the direction of the graph of \(f(x)=-3x^{2}+5x-4\) without even graphing it?
- Use Desmos to find the following characteristics of \(g(x)=2x^{2}-8x+3\).
- Vertex
- Axis of symmetry
- y-intercept
- x-intercepts
- Domain
- Range
- The daily profit for a manufacturing company is modeled by the function \(P(x)=-0.6x^{2}+168x-9375\), where \(x\) is the number of items manufactured.
- What is the company's profit if zero items are manufactured in a day?
- What is the company's profit if 90 items are manufactured in a day?
- What is the range of items that must be made each day in order to make any profit?
- What is the maximum daily profit they can make, and how many items do they need to manufacture in order to make that profit?
- What do the x-intercepts of the graph represent in this scenario?