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Study Guides > MATH 1314: College Algebra


Solutions to Try Its

1. Graph of the line y = (3/4)x + 6, with the points (0,6), (4,3) and (8,0) labeled. 2. Possible answers include [latex]\left(-3,7\right)\\[/latex], [latex]\left(-6,9\right)\\[/latex], or [latex]\left(-9,11\right)\\[/latex]. 3. 4. [latex]\left(16,\text{ 0}\right)\\[/latex] 5. a. [latex]f\left(x\right)=2x\\[/latex] b. [latex]g\left(x\right)=-\frac{1}{2}x\\[/latex] 6. [latex]y=-\frac{1}{3}x+6\\[/latex] 7.

a. [latex]\left(0,5\right)\\[/latex]

b. [latex]\left(5,\text{ 0}\right)\\[/latex]

c. Slope -1

d. Neither parallel nor perpendicular

e. Decreasing function

f. Given the identity function, perform a vertical flip (over the t-axis) and shift up 5 units.

Solutions to Odd-Numbered Exercises

1. The slopes are equal; y-intercepts are not equal. 3. The point of intersection is [latex]\left(a,a\right)\\[/latex]. This is because for the horizontal line, all of the y coordinates are a and for the vertical line, all of the x coordinates are a. The point of intersection will have these two characteristics. 5. First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation [latex]y=mx+b\\[/latex] and solve for b. Then write the equation of the line in the form [latex]y=mx+b\\[/latex] by substituting in m and b. 7. neither parallel or perpendicular 9. perpendicular 11. parallel 13. [latex]\left(-2\text{, }0\right)\\[/latex] ; [latex]\left(0\text{, 4}\right)\\[/latex] 15. [latex]\left(\frac{1}{5}\text{, }0\right)\\[/latex] ; [latex]\left(0\text{, 1}\right)\\[/latex] 17. [latex]\left(8\text{, }0\right)\\[/latex] ; [latex]\left(0\text{, }28\right)\\[/latex] 19. [latex]\text{Line 1}: m=8 \text{ Line 2}: m=-6 \text{Neither}\\[/latex] 21. [latex]\text{Line 1}: m=-\frac{1}{2} \text{ Line 2}: m=2 \text{Perpendicular}\\[/latex] 23. [latex]\text{Line 1}: m=-2 \text{ Line 2}: m=-2 \text{Parallel}\\[/latex] 25. [latex]g\left(x\right)=3x - 3\\[/latex] 27. [latex]p\left(t\right)=-\frac{1}{3}t+2\\[/latex] 29. [latex]\left(-2,1\right)\\[/latex] 31. [latex]\left(-\frac{17}{5},\frac{5}{3}\right)\\[/latex] 33. F 35. C 37. A 39. 41. 43. 45. 47. 49. 51. 53. 55. 57. 59. [latex]g\left(x\right)=0.75x - 5.5\text{}\\[/latex] 0.75 [latex]\left(0,-5.5\right)\\[/latex] 61. [latex]y=3\\[/latex] 63. [latex]x=-3\\[/latex] 65. no point of intersection 67. [latex]\left(\text{2},\text{ 7}\right)\\[/latex] 69. [latex]\left(-10,\text{ }-5\right)\\[/latex] 71. [latex]y=100x - 98\\[/latex] 73. [latex]x<\frac{1999}{201}x>\frac{1999}{201}\\[/latex] 75. Less than 3000 texts  

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  • Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..