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

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

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

Summary of Graphs of Common Functions f(x) = c y = x y = x 2 y = x 3

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

Graph Graph the two linear functions y x 2 -2 y x 2 y x 2

Graph Graph the two linear functions y x 2 -2 y x 2 y x 2

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