2.2E: Graphs of Linear Functions (Exercises)

Last updated
Save as PDF

Page ID: 13898

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$ \newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\id}{\mathrm{id}}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\kernel}{\mathrm{null}\,}$

$ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$

$ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$

$ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\AA}{\unicode[.8,0]{x212B}}$

$ \newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$ \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$ \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vectorC}[1]{\textbf{#1}} $

$ \newcommand{\vectorD}[1]{\overrightarrow{#1}} $

$ \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} $

$ \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} $

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y}$ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real}{\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var}{\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left|#1\right|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$

Section 2.2 exercise

Match each linear equation with its graph

$屏幕快照 2019-06-18 下午10.14.16.png$

1. $f(x)=-x-1$

2. $f(x)=-2x-1$

3. $f(x)=-\dfrac{1}{2} x-1$

4. $f(x)=2$

5. $f(x)=2+x$

6. $f(x)=3x+2$

Sketch a line with the given features

7. An x-intercept of (-4, 0) and y-intercept of (0, -2)

8. An x-intercept of (-2, 0) and y-intercept of (0, 4)

9. A vertical intercept of (0, 7) and slope $-\dfrac{3}{2}$

10. A vertical intercept of (0, 3) and slope $\dfrac{2}{5}$

11. Passing through the points (-6,-2) and (6,-6)

12. Passing through the points (-3,-4) and (3,0)

Sketch the graph of each equation

13. $f(x)=-2x-1$

14. $g(x)=-3x+2$

15. $h(x)=\dfrac{1}{3} x+2$

16. $k(x)=\dfrac{2}{3} x-3$

17. $k(t)=3+2t$

18. $p(t)=-2+3t$

19. $x=3$

20. $x=-2$

21. $r(x)=4$

22. $q(x)=3$

23. If $g(x)$ is the transformation of $f(x)=x$ after a vertical compression by $3/4$, a shift left by 2, and a shift down by 4

a. Write an equation for $g(x)$
b. What is the slope of this line?
c. Find the vertical intercept of this line.

24. If $g(x)$ is the transformation of $f(x)=x$ after a vertical compression by $1/3$, a shift right by 1, and a shift up by 3

a. Write an equation for $g\left(x\right)$
b. What is the slope of this line?
c. Find the vertical intercept of this line.

Write the equation of the line shown

25. $屏幕快照 2019-06-18 下午10.20.23.png$ 26. $屏幕快照 2019-06-18 下午10.21.50.png$

27. $屏幕快照 2019-06-18 下午10.23.34.png$ 28. $屏幕快照 2019-06-18 下午10.23.56.png$

Find the horizontal and vertical intercepts of each equation

29. $f(x)=-x+2$

30. $g(x)=2x+4$

31. $h(x)=3x-5$

32. $k(x)=-5x+1$

33. $-2x+5y=20$

34. $7x+2y=56$

Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular or neither?

35. Line 1: Passes through $(0,6)$ and $(3,-24)$
Line 2: Passes through $(-1,19)$ and $(8,-71)$

36. Line 1: Passes through $(-8, -55)$ and $(10, 89)$
Line 2: Passes through $(9, -44)$ and $(4,-14)$

37. Line 1: Passes through $(2,3)$ and $(4,-1)$
Line 2: Passes through $(6,3)$ and $(8,5)$

38. Line 1: Passes through $(1, 7)$ and $(5,5)$
Line 2: Passes through $(-1,-3)$ and $(1,1)$

39. Line 1: Passes through $(0, 5)$ and $(3,3)$
Line 2: Passes through $(1,-5)$ and $(3,-2)$

40. Line 1: Passes through $(2,5)$ and $(5,-1)$
Line 2: Passes through $(-3,7)$ and $(3,-5)$

41. Write an equation for a line parallel to $f(x)=-5x-3$ and passing through the point (2,-12)

42. Write an equation for a line parallel to $g(x)=3x-1$ and passing through the point (4,9)

43. Write an equation for a line perpendicular to $h(t)=-2t+4$ and passing through the point (-4,-1)

44. Write an equation for a line perpendicular to $p(t)=3t+4$ and passing through the point (3,1)

45. Find the point at which the line $f(x)=-2x-1$ intersects the line $g(x)=-x$

46. Find the point at which the line $f(x)=2x+5$ intersects the line $g(x)=-3x-5$

47. Use algebra to find the point at which the line $f(x)= -\dfrac{4}{5} x +\dfrac{274}{25}$ intersects the line $h(x)=\dfrac{9}{4} x +\dfrac{73}{10}$

48. Use algebra to find the point at which the line $f(x)=\dfrac{7}{4} x +\dfrac{457}{60}$ intersects the line $g(x)=\dfrac{4}{3} x +\dfrac{31}{5}$

49. A car rental company offers two plans for renting a car.
Plan A: 30 dollars per day and 18 cents per mile
Plan B: 50 dollars per day with free unlimited mileage
How many miles would you need to drive for plan B to save you money?

50. You’re comparing two cell phone companies.
Company A: $20/month for unlimited talk and text, and $10/GB for data.
Company B: $65/month for unlimited talk, text, and data.
Under what circumstances will company A save you money?

Find a formula for each piecewise defined function.

51. $屏幕快照 2019-06-18 下午10.32.41.png$ 52. $屏幕快照 2019-06-18 下午10.33.00.png$

53. Sketch an accurate picture of the line having equation $f(x)=2-\dfrac{1}{2} x$. Let $c$ be an unknown constant. [UW]

a. Find the point of intersection between the line you have graphed and the line $g(x)=1+cx$; your answer will be a point in the $xy$ plane whose coordinates involve the unknown $c$.
b. Find $c$ so that the intersection point in (a) has $x$-coordinate 10.
c. Find $c$ so that the intersection point in (a) lies on the $x$-axis.

Answer

1. E

3. D

5. B

7. $Screen Shot 2019-10-01 at 9.42.46 AM.png$