1. Sec. 2.4 Library of Functions

2. 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

3. 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

4. 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

5. 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

6. 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)

7. 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

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

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

10. 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, ∞)

11. 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

12. 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

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

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