1. Comparing
Linear,
Exponential,
and
Quadratic Functions

2. Identifying from an equation:
Linear y = mx +b Has an x with no exponent (or exponent 1). Examples: y = 5x + 1 y = ½x 2x + 3y = 6
Quadratic y = ax2 + bx + c Has an x2 in the equation. Examples: y = 2x2 + 3x – 5 y = x2 + 9 x2 + 4y = 7
Exponential y = abx Has an x as the exponent. Examples: y = 3x + 1 y = 52x 4x + y = 13

3. Examples: LINEAR, QUADRATIC or EXPONENTIAL? y = 6x + 3 y = 7x2 +5x – 2

4. Identifying from a graph:
Linear Makes a straight line
Quadratic Makes a U or ∩
Exponential Rises or falls quickly in one direction

5. LINEAR, QUADRATIC, EXPONENTIAL, OR NEITHER?
a) b)
c) d)

6. Is the table linear, quadratic or exponential?
y changes more quickly than x.
Never see the same y value twice.
Can be written as:
Next = Now  b,
y-intercept: a
Quadratic
See same y more than once.
Linear
Never see the same y value twice.
Can be written as: Next = Now + m,
y-intercept: b

7. Identifying functions given a table of values
EXAMPLE 1
Identifying functions given a table of values b. x
– 2
– 1 1 2 y 4 7 10
Next = Now + 3, y-int: 4  y = 3x +4  Linear Function

8. Identifying functions given a table of values
EXAMPLE 2
Identifying functions given a table of values
Does the table of values represent a linear function, an exponential function, or a quadratic function? a. x –2 –1 1 2 y
0.25
0.5 4
Next = Now  2, y-int: 1  y = 1(2)x  Exponential Function

9. Identifying functions given a table of values
EXAMPLE 3
Identifying functions given a table of values
Determine which type of function the table of values represents. x –2 –1 1 2 y
0.5
– –
Notice that there are two y-values associated with an x-value: (-2,2) and (2,2)  Quadratic Function

10. Is the table linear, quadratic or exponential?y 1 2 -1 3 4 5 8 x y 1 3 2 9 27 4 81 5
243 x y 1 5 2 9 3 13 4 17 21

11. Identifying Regressions Using Shapes of Known Functions

12. Fitting Functions to Data
The term regression pertains to the process of finding an equation for the relationship seen in a scatter plot. Regression is a generic term for all methods attempting to fit a model to observed data in order to predict new values. Steps for finding a regression: 1. Create a scatter plot:

13. Creating a Scatter Plot
9 Zoom Stat

14. Go to STAT, arrow right to CALC, and arrow down for regression equation choices.

17. Practice: