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# Solutions

## Solutions to Try Its

1. 2. Possible answers include $\left(-3,7\right)\\$, $\left(-6,9\right)\\$, or $\left(-9,11\right)\\$. 3. 4. $\left(16,\text{ 0}\right)\\$ 5. a. $f\left(x\right)=2x\\$ b. $g\left(x\right)=-\frac{1}{2}x\\$ 6. $y=-\frac{1}{3}x+6\\$ 7.

a. $\left(0,5\right)\\$

b. $\left(5,\text{ 0}\right)\\$

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 $\left(a,a\right)\\$. 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 $y=mx+b\\$ and solve for b. Then write the equation of the line in the form $y=mx+b\\$ by substituting in m and b. 7. neither parallel or perpendicular 9. perpendicular 11. parallel 13. $\left(-2\text{, }0\right)\\$ ; $\left(0\text{, 4}\right)\\$ 15. $\left(\frac{1}{5}\text{, }0\right)\\$ ; $\left(0\text{, 1}\right)\\$ 17. $\left(8\text{, }0\right)\\$ ; $\left(0\text{, }28\right)\\$ 19. $\text{Line 1}: m=8 \text{ Line 2}: m=-6 \text{Neither}\\$ 21. $\text{Line 1}: m=-\frac{1}{2} \text{ Line 2}: m=2 \text{Perpendicular}\\$ 23. $\text{Line 1}: m=-2 \text{ Line 2}: m=-2 \text{Parallel}\\$ 25. $g\left(x\right)=3x - 3\\$ 27. $p\left(t\right)=-\frac{1}{3}t+2\\$ 29. $\left(-2,1\right)\\$ 31. $\left(-\frac{17}{5},\frac{5}{3}\right)\\$ 33. F 35. C 37. A 39. 41. 43. 45. 47. 49. 51. 53. 55. 57. 59. $g\left(x\right)=0.75x - 5.5\text{}\\$ 0.75 $\left(0,-5.5\right)\\$ 61. $y=3\\$ 63. $x=-3\\$ 65. no point of intersection 67. $\left(\text{2},\text{ 7}\right)\\$ 69. $\left(-10,\text{ }-5\right)\\$ 71. $y=100x - 98\\$ 73. $x<\frac{1999}{201}x>\frac{1999}{201}\\$ 75. Less than 3000 texts

## Licenses & Attributions

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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]..