1. 3x + 2 = ½ x – 5
2. |3x + 2| > 12
3. 4x – 5 < -3x + 2
4. |x + 2| < 15
Algebra II 1
Algebra II
Transformations of parent functions
Parent function: the most basic graph in a family of graphs
Transformation A change in size, shape, position, or
orientation of a graph Translation
A transformation that shifts a graph horizontally or vertically but does not change size or shape
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Reflection A transformation that flips a graph over a line of
reflection Vertical stretch
A transformation that causes the graph of a function to stretch away from the x axis. (multiplied by a factor >1)
Vertical shrink A transformation that causes the graph of a
function to shrink toward the x-axis (multiplied by a factor 0<a<1)
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Domain: The x values of a graph, the distance from left to right
Range: the y values of a graph, the distance from bottom to top
** Domain and Range must be written in: INTERVAL NOTATION
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Domain: [-4,-1]
Range: [-4,∞)
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Domain: [-1,5]
Range: [-4,7]
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Domain: (-∞, ∞)
Range: [0,∞)
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Algebra II 9
Constant Linear
f(x) = 1
Domain: (-∞,∞)
Range {1}
f(x) = x
Domain: (-∞,∞)
Range: (-∞,∞)
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Absolute Value Quadratic
f(x) = |x|
Domain: (-∞,∞)
Range: [0, ∞)
f(x) = x2
Domain: (-∞,∞)
Range: [0, ∞)
RxSRy
Reflect over x-axis (affect the y-values), Shift (horizontal and vertical),
Reflect over y-axis (affect the x-values) y = -(x) effects y so flips over x axis y = (x – h) effects x: shift left/right (opposite
direction) y = x + k effects y: shift up/down (same
direction) y =(-x) effects x so reflect over y
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Algebra II 12
Linear f(x) = x
Vertical Shrink by a factor of ¼
Reflection over the x-axis
Vertical shift up 8
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Constant f(x) = 1
Vertical shift down 4
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Absolute Value f(x) = |x|
Horizontal shrink by a Factor of ⅕…….SoIt is also a vertical stretch by a factor of 5
NARROWER
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Quadratic f(x) = x2
Horizontal shift right 1
Vertical shift up 4
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Linear f(x) = x
Vertical shift down 7
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Constant f(x) = 1
Vertical shift down10
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Absolute Value f(x) = |x|
Vertical shiftUp 1
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Quadratic f(x) = x2
Reflection overthe x-axis
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Quadratic f(x) = x2
Vertical shrink bya factor of ⅛
WIDER
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Absolute Value f(x) = |x|
Vertical stretch by a factor of 6 NARROWER
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11. Identify the function family of f(x) = ⅓|-x| + 4 and describe the domain and range. Use a graphing calculator to verify your answers.
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11b. Identify the function family of f(x) = -2(x + 3)2 – 8 and describe the domain and range. Use a graphing calculator to verify your answers.
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13.
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14.
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15.
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16. Graph g(x) = x – 4 and its parent function. Then describe the transformation.
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17.
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18. Graph p(x) = -x2 and its parent function. Then describe the transformation.
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19. Graph k(x) = -x and its parent function. Then describe the transformation.
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21. g(x) = x + 3
22. h(x) = (x – 2)2
20. m(x) = -|x|
23. g(x) = 2|x|
24. h(x) = ½x2
25. g(x) = 3x
26. h(x) = 3/2x2 + 3
27. c(x) = 0.2 |x – 2|
28. g(x) = - |x + 5| - 3
29. h(x) = -0.25x2 + 4
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31. The table shows the height y of a dirt bike x seconds after jumping off a ramp. What type of function can you use to model this data? Estimate the height after 1.75 seconds.
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Use a graphing calculator to graph the function and its parent function. Then describe the transformation.
32. h(x) = -¼x + 5 33. d(x) = 3(x – 1)2 - 1
34.
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35.
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Identify the function family to which g belongs. Compare the graph of g to itsparent function and describe the transformation.
1. g(x) = -x + 2
2. g(x) = x2 - 2
3. g(x) = 2 – 0.2x
4. g(x) = 2 I x I - 2
5. g(x) = 2.2(x + 2)2
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6.