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The Linear Parent Function

The Linear Parent Function. y=x. The Linear Parent Function. What is a linear parent function ? The linear parent function is the most basic form of a linear function. y=x m=1 b=0 What are the characteristics of the linear parent function? The rate of change is 1 The y-intercept is 0

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The Linear Parent Function

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  1. The Linear Parent Function y=x

  2. The Linear Parent Function • What is a linear parent function? • The linear parent function is the most basic form of a linear function. • y=x • m=1 • b=0 • What are the characteristics of the linear parent function? • The rate of change is 1 • The y-intercept is 0 • Goes through the point (0,0) • Slope is up 1, right 1

  3. The Linear Parent Function y=x

  4. The Linear Parent Function Changing the y-intercept

  5. y=x to y=x+3 Add 3 Shift Up 3 y=x

  6. y=x to y=x-3 Subtract 3 Shift Down 3 y=x

  7. y=x to y=x+5 Add 5 Shift Up 5 y=x

  8. y=x-3 to y=x+7 Add 10 Shift Up 10

  9. y=x+4 to y=x-1 Subtract 5 Shift Down 5

  10. y=x to y=x+7 Add 7 Shift Up 7

  11. Without the Graph – Describe what will happen graphically y=x+3 to y=x+6

  12. Without the Graph – Describe what will happen graphically Add 12 to the y-intercept

  13. Without the Graph – Describe what will happen graphically Subtract 15 from the y-intercept

  14. The Linear Parent Function Changing the Slope

  15. y=5x y=x to y=5x y=x to y=3x 3 is greater than 1, so the line gets steeper. 5 is greater than 1 and 3, so the line gets steeper. y=x y=3x

  16. y=-x Estimate y=-3x y=-5x y=-.5x y=-x

  17. The Linear Parent Function Change m and b

  18. y=3x+2 to y=2x+5 Add 3 Shift Up 3 Change Slope y=3x+2

  19. Without the Graph – Describe what will happen graphically y=3x-2 to y=4x-3

  20. Without the Graph – Describe what will happen graphically y=5x+7 to y=5x+6

  21. A florist charges $25 for a vase plus $4.50 for each flower. The total charge for the vase and flowers is given by the function f(x) = 4.50x + 25. How will the graph change if the vase’s cost is raised to $35? if the charge per flower is lowered to $3.00? f(x) = 4.50x + 25 is graphed in blue. Total Cost If the vase’s price is raised to $35, the new function is f(g) = 4.50x + 35. The original graph will be translated 10 units up.

  22. A florist charges $25 for a vase plus $4.50 for each flower. The total charge for the vase and flowers is given by the function f(x) = 4.50x + 25. How will the graph change if the vase’s cost is raised to $35? If the charge per flower is lowered to $3.00? If the charge per flower is lowered to $3.00. The new function is h(x) = 3.00x + 25. The original graph will be rotated clockwise about (0, 25) and become less steep. Total Cost

  23. What if…? How will the graph change if the charge per letter is lowered to $0.15? If the trophy’s cost is raised to $180? f(x) = 0.20x + 175 is graphed in blue. If the charge per trophy is raised to $180. The new function is h(x) = 0.20x + 180. The original graph will be translated 5 units up. Cost of Trophy If the cost per letter charged is lowered to $0.15, the new function is g(x) = 0.15x + 175. The original graph will be rotated around (0, 175) and become less steep.

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