Sec. 2.4 Library of Functions

Types of functions Linear (2 special types) Squaring (quadratic) Cubic Constant Identity Squaring (quadratic) Cubic Square root Reciprocal Step function (most common Greatest Integer Function Piecewise

Linear f(x) = mx + b Domain Range Intercepts m = slope b is the y – intercept (0,b) Domain All real numbers Range Intercepts 1 x – intercept 1 y - intercept

Can tell if increasing or decreasing by the slope m > 0 (positive) Increasing m < 0 (negative) decreasing m = 0 Constant (horizontal) m is undefined vertical

To write a linear equation you need the slope and either the y int To write a linear equation you need the slope and either the y int. or a point on the line. Ex. 1 Write an equation for f(1) = 3 and f(4) = 0

2 Special linear functions Constant function f(x) = c (or y = c) horizontal Identity function f(x) = x (or y = x) Slope of 1 Intercept at (0,0)

Squaring Function (Quadratic) f(x) = x2 (parabola) Domain All real numbers Range All non-negative real numbers Even Symmetric with respect to the y axis Intercept (0,0) Decreasing (-∞, 0) Increasing (0, ∞) Relative Minimum

Cubic f(x) = x3 Domain Range Odd Intercept Increasing All real numbers Symmetric with respect to the origin Intercept (0,0) Increasing (-∞, ∞)

Square Root F(x) = √x Domain Range Intercept Increasing All non-negative real numbers Range Intercept (0,0) Increasing (0, ∞)

Reciprocal f(x) = 1/x Domain Range Odd No intercepts Decreasing (-∞, 0) ⋃ (0, ∞) Range Odd Symmetric with respect to the origin No intercepts Decreasing (-∞, 0) and (0, ∞)

Step Function (greatest integer function) Represented by〚x〛 Means the greatest integer less than or equal to x P. 214 figure 2.43 Jumps up vertically 1 unit at each integer Constant (horizontal) between each pair of consecutive integers

Constant between consecutive integers Domain All real numbers Range All integers Y intercept (0,0) X intercept Interval [0,1) Constant between consecutive integers Jumps vertically 1 unit at each integer

EX. P. 215 Evaluate when x = -1, 2, and 3/2

Piecewise function Look at ex. 3 p. 216 Pieces of different functions Look at common functions p. 216