The Graph Below Belongs to Which Function Family

**Chapter 1 Review** In Exercises 1 and 2, identify the function family to which f belongs. Compare the graph of f to the graph of its parent function. 1. [Image of a parabola opening upwards, shifted one unit up] Parent Function: Quadratic Transformation: Vertical shift up 1 unit 2. [Image of a horizontal line at y = 2] Parent Function: Constant function Transformation: Shifted up one unit In Exercises 3-11, graph the function and its parent function. Then describe the transformation. 3. f(x) = x + 2 [Image of a line with a slope of 1, shifted up 2 units] Shifted up 2 units 4. f(x) = x - 3 [Image of a line with a slope of 1, shifted down 3 units] Shifted down 3 units 5. f(x) = x + 2 [Image of a line with a slope of 1, shifted up 2 units] Shifted up 2 units 6. f(x) = (x - 1)^2 [Image of a parabola opening upwards, shifted right 1 unit] Shifted right 1 unit 7. f(x) = 1/2x - 1 [Image of a line with a slope of 1/2, shifted down 1 unit] Compressed vertically by a factor of 1/2, shifted down 1 unit 8. f(x) = x + 3 [Image of a line with a slope of 1, shifted up 3 units] Shifted up 3 units 9. f(x) = |3x - 1| + 7 Vertical Stretch Shift Up 7 10. f(x) = 2x^5 Vertical Stretch 11. f(x) = 1/x^2 Vertical Shift Up 4 Units Write a function g whose graph represents the indicated transformation of the graph of f. 12. f(x) = x + 1; translation 2 units right g(x) = (x - 2) + 1 = x - 1 13. f(x) = |3x + 2| + 4; translation 3 units left g(x) = |3(x + 3) + 2| + 4 = |3x + 11| + 4 14. f(x) = x^2; reflection in the x-axis, down 3 g(x) = -x^2 - 3 15. f(x) = x; vertical stretch by a factor of 4 g(x) = 4x 16. f(x) = x^2; translation 3 units left, followed by a horizontal shrink by a factor of 1/2 **Do Not Do** 17. f(x) = x; vertical shrink by a factor of 1/3, followed by a translation 4 units down g(x) = (1/3)x - 4 18. f(x) = |x|; translation 3 units left, followed by a horizontal shrink by a factor of 1/2 **Do Not Do** **For Exercises 19 and 20, use the graph to write an equation of the line and interpret the slope.** **19. Hotel Stay** [Image of a line graph with points (50, 100) and (125, 12)] Equation: y = 3/5x + 10 Shape: As the cost of the room increases, so does the sales tax. Each additional dollar of cost increases the sales tax by $0.60. **20. Soap in Bottle** [Image of a line graph with points (0, 10) and (20, 0)] Equation: y = -1/2x + 10 Slope: -1/2. Each day you use the soap, the amount of soap decreases by 1/2 ounce. **Determine whether the data show a linear relationship. If so, write an equation of a line of fit. Estimate y when x = 15 and explain its meaning in the context of the situation.** 21. | Weeks, x | 3 | 6 | 10 | 12 | 16 | |---|---|---|---|---|---| | Height of basil plant (inches), y | 2 | 5 | 9 | 15 | 21 | Not Linear 22. | Days, x | 3 | 7 | 11 | 14 | 20 | |---|---|---|---|---|---| | Number of tickets sold, y | 76 | 104 | 152 | 184 | 250 | y = 22x + 10 Every day there are 22 tickets sold and after 15 days there was 340 tickets sold. 23. | Minutes running, x | 10 | 17 | 25 | 35 | 40 | |---|---|---|---|---|---| | Calories burned, y | 70 | 118 | 200 | 295 | 472 | y = 12x - 2 Every minute you run you burn 12 calories and after 15 minutes you burn 178 calories. **Solve the system using the elimination method. (If you need more room, use the back of the paper.)** 24. x - 6y + 2z = 5 2x - 5y + z = 4 3x + 4y - 2z = -2 -> x - 6y + 2z = 5 -> 3x - 18y + 6z = 15 -> 3x + 4y - 2z = -2 -> 9y - 3z = -6 -> -21y + 1z = 14 -> 3y - z = -2 -> -21y + z = 14 -> -18y = 12 -> y = -3 x - 6(-3) + 2(-7) = 5 x + 18 - 14 = 5 x + 4 = 5 x = 1 **Solution: (1, -3, -7)** 25. x + 4y - 3z = 1 3x + 12y - 9z = 8 2x + 4y - 4z = -12 -> -3x - 12y + 9z = -3 -> 3x + 12y - 9z = 8 -> 0 = 5 **No Solution**