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.

m0 34 1

1

Next, use the point-slope form of the equation of a line.

y y1 m(x x1)

y 3 1(x 1)

Function notation.

f (x) x 4

Cubic, Square Root, and Reciprocal Functions

The graph of the cubic function f(x) = x3 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.

y 1x

• 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, ∞)

xy

Summary of Graphs of Common Functions

f(x) = c

y = x xy

xy y = x2y = x 3

The graph of the greatest integer function.

xxf )( Greatest integer less than the value given by x

Graph

• Graph the two linear functions

2 3, x 1( )

4; x>1x

f xx

y

x

2

-2

y

x

2

-2

y

x

2

-2

Graph

• Graph the two linear functions

2 3, x 1( )

4; x>1x

f xx

y

x

2

-2

y

x

2

-2

y

x

2

-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