1. Today’s Lesson: Comparing Linear, Quadratic, & Exponential Functions
December,14, 2017

2. Linear Function Basic Algebraic Form:
Slope-intercept form is y = mx + b

3. Linear Functions
y = 3x + 5 X -1 1 2 Y 5 8 11
When the function is linear then there is a constant difference between each of the y values & x-values (SAME SLOPE!)

4. Word Problem - Linear
ABC bowling charges $5 for shoe rental and then an additional $3 per game bowled. If Chelsie bowls 4 games, how much will she have to pay?

5. Exponential Function
Basic Algebraic Form:

6. Exponential Functions
Y =0.5(2)x X -1 1 2 Y
0.25
0.5
If you notice the differences are not the same, then try dividing the y values to find a common ratio.

7. Word Problem – Exponential
A colony of bacteria has a mass grams and doubles every hour. How much will the colony of bacteria weigh after 6 hours?

8. Quadratic Functions

9. Quadratic Functions Y = x2 – 2x + 0 X -1 1 2 3 Y1 2 3 Y
If the differences are not the same. (3 - 0 = 3, and = 1) And the ratios are not the same ( 0/3 = 0 and -1/0 = undefined). Then this function is neither linear nor exponential.
*But if the second differences are the same then the function is quadratic.

10. Word Problem – Quadratic
The product of a number and the number minus four is -3. What is the number?

11. Identifying from an equation:
Linear
Has an x with no exponent.
y = 5x + 1
y = ½x
2x + 3y = 6
Quadratic
Has an x2 in the equation.
y = 2x2 + 3x – 5
y = x2 + 9
x2 + 4y = 7
Exponential Has an x as the exponent. y = 3x + 1 y = 52x 4x + y = 13

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

14. Using differences and ratios to tell whether the values in the table represent a linear, exponential or quadratic function. X 1 2 3 4 Y -1 -2 -3 X -2 -1 1 2 Y -4 X -1 1 2 3 Y 16 4
1/16 X -3 -2 -1 1 Y
13.5 6
1.5

15. A chambered nautilus is a marine animal that lives in the outermost chamber of its shell. When the Nautilus outgrows a chamber it adds a new, larger chamber to its shell. The table shows the volumes (in cubic cm) of consecutive chambers of a nautilus. Tell whether the data can be modeled by a linear function, an exponential function, or a quadratic function.
Chamber 1 2 3 4 5 6
Volume (cm3)
0.837
0.889
0.945
1.005
1.068
1.135

16. The table shows the body temperature B (in degrees Celsius) of a desert spiny lizard at various air temperatures A (in degrees Celsius) Tell whether the data can be modeled by a linear function, an exponential function, or a quadratic function.
Air Temp, A (ºC) 26 27 28 29 30
Body Tem (ºC)
33.44
33.78
34.12
34.46
34.80

17. The time it takes for a clock’s pendulum to swing from one side to another and back again is called the pendulums period. The table shows the period t (in seconds) of a pendulum of length l (in feet). Tell whether the data can be modeled by a liner function, and exponential function or a quadratic function.
Period, t(sec) 1 2 3 4 5
Length, l (ft)
0.82
3.28
7.38
13.12
20.5

18. 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

21. Comparing Functions Worksheet
Homework
Comparing Functions Worksheet