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1.6 A Library of Parent Functions

1.6 A Library of Parent Functions. Ex. 1 Write a linear function for which f(1) = 3 and f(4) = 0. First, find the slope. Next, use the point-slope form of the equation of a line. Function notation. Cubic, Square Root, and Reciprocal Functions.

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1.6 A Library of Parent Functions

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  1. 1.6 A Library of Parent Functions Ex. 1 Write a linear function for which f(1) = 3 and f(4) = 0 First, find the slope. Next, use the point-slope form of the equation of a line. Function notation.

  2. Cubic, Square Root, and Reciprocal Functions The graph of the cubic function f(x) = x3 has the following features. • Domain and Range = • The function is odd. • The graph goes thru (0,0) • It is increasing from • Symmetric about the origin. y = x 3

  3. The graph of the reciprocal function. • Domain and Range • (-∞, 0)  (0, ∞) • Odd function • No intercepts • Decreasing (-∞, 0) and (0, ∞) • Symmetric to origin

  4. The graph of the square root function. • Domain and Range • nonnegative real numbers • Intercept at (0, 0) • Increasing (0, ∞)

  5. Summary of Graphs of Common Functions f(x) = c y = x y = x 3 y = x2

  6. The graph of the greatest integer function. Greatest integer less than the value given by x

  7. y y y 2 2 2 x x x -2 -2 -2 Graph • Graph the two linear functions

  8. y y y 2 2 2 x x x -2 -2 -2 Graph • Graph the two linear functions

  9. Evaluate the function when x = -1, -2.3 and 3/2 f(x) = ║x║ + 1 f(–1) = ║–1║ + 1 = –1 + 1 = 0 f(–2.3) = ║–2.3║ + 1 = –3 + 1 = –2 f(1.5) = ║1.5║ + 1 = 1 + 1 = 2

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