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Library of Functions

Library of Functions. You should be able to graph the functions listed in the Library of functions. Properties of f (x) =. The x intercept of the graph of f(x) = is (0,0). The y intercept of the graph is (0,0) The function is neither even nor odd

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Library of Functions

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  1. Library of Functions You should be able to graph the functions listed in the Library of functions

  2. Properties of f (x) = The x intercept of the graph of f(x) = is (0,0). The y intercept of the graph is (0,0) The function is neither even nor odd It is increasing on the interval (0,∞) It has no local minimum of 0 at x=0

  3. Properties of • The x intercept of the graph of f(x) is 0 • The y intercept of the graph is also 0 • It is increasing on the interval (-∞,∞) • It does not have a local minimum or a local maximum

  4. Properties of f(x)= │x│ • The x intercept of the graph of f(x) = │x │is 0. The y intercept of the graph of f(x) is also 0 • The function is even • It is decreasing on the interval (-∞,0). It is increasing on the interval (0,∞) • It has a local minimum of 0 at x=0

  5. Library of functions Linear Function: f(x) = mx+b Constant Function: f(x)= b Identity Function: f(x) = x Square function: f(x) = x2

  6. Cube Function f(x) = x3

  7. Reciprocal Function f(x)=

  8. Graphing Techniques: Transformations Graph Functions Using Horizontal and Vertical Shifts Graph Functions Using Compressions and Stretches Graph Functions Using Reflections about the x axis and the y axis

  9. Activity On your graphing utility graph f(x)= x2 In your Y2 graph the following functions and describe what happens to the graph. F(x) = x2 +3 F(x) = -x2 F(x) = x2-4 F(x) = (-x)2 F(x) = (x – 1)2 F(x) = (2x)2 F(x) = (x + 2)2 F(x) =( x)2 F(x) = 2x2 F(x) =

  10. Vertical Shifts If a real number k is added to the right side of a function y= f(x) the graph of the new function y=f(x) +k is the graph of f shifted vertically up if k>0 or down if k<0.

  11. Horizontal Shifts If the argument x of a function f is replaced with (x-h) , h a real number, the graph of the new function y= f(x-h) is the graph of f shifted horizontally left if h<0 or right if h>0

  12. Vertical Stretch or Compression When the right side of a function y=f(x) is multiplied by a positive number a, the graph of the new function y= af(x) is obtained by multiplying each y coordinate of y= f(x) by a . A vertical compression results if 0<a<1 and a vertical stretch occurs if a>1.

  13. Horizontal Compression and Stretch If the argument x of a function y=f(x) is multiplied by a positive number a, the graph of the new function y= f(ax) is obtained by multiplying each x coordinate of y= f(x) by A horizontal compression results if a>1, and a horizontal stretch and a horizontal stretch occurs if 0 < a <1.

  14. Translations and Reflections • Equation • y= f(x) +k the graph shifts up k units • y=f(x) –k the graph shifts down k units • y=f(x-c) the graph shifts to the right c units • y= f(x+c) the graph shifts to the left c units • y= -f(x) reflect in the x axis • y=f(-x) reflect in the y axis • y = f(ax) multiply your x values by 1/a • a> 1 the graph compresses horizontally • 0<a<1 the graph stretches horizontally • y =af(x) multiply your y values by a • a>1 stretch vertically • 0<a<1 compress vertically

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