Linear Models
Quadratic Models
Exponential Models
Which one?
Average Rate of Change
100
Which of these graphs shows a linear function?
f(x) g(x) h(x)
h(x)
100
Which of these graphs shows a quadratic function?
f(x) g(x) h(x)
f(x)
100
Which of these graphs shows a exponential function?
f(x) g(x) h(x)
g(x)
100
If the x-variable is time (seconds) and the y-variable is distance in (meters), what is an appropriate term for the rate of change?
*remember change in y over change in x
seconds per meter
100
f(x) = 2x2 + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].
A) 2
B) 1/2
C) -2
D) -1/2
A) 2
200
In order to calculate if a function is linear, we have to look at the _______?
A) First Differences
B) Second Differences
C) Ratios
First Differences
200
In order to calculate if a function is quadratic, we have to look at the _______?
A) First Differences
B) Second Differences
C) Ratios
Second Differences
200
In order to calculate if a function is exponential, we have to look at the _______?
A) First Differences
B) Second Differences
C) Ratios
Ratios
200
Determine if this data belongs to a function that is linear, quadratic or exponential.
Linear because the first differences are the same.
200
What is the average rate of change of y = 2(3)x at x = 2 to x = 4 ?
A) 72 B) 3
C) 36.8 D) 630
A) 72
300
True or False.
A linear relationship implies different changes over equal intervals.
False.
A linear relationship implies equal changes over equal intervals.
300
Is the rate of change for this function positive or negative over the interval 2 < x < 3?
Decreasing
300
True of False
In an exponential relation, there is a constant percent increase/decrease over equal intervals.
True
300
True or False
This table of values shows the data of a quadratic function.
True
300
What is Mrs. Gordons rate from 0 to 2 seconds?
2.5 feet per second
400
If the a linear function is y=3x + 5, predict what the function will be at x=20
y=3(20) + 5
y=60 + 5
y=65
400
If a quadratic function is y=3x2+2x+5, predict what the function will be at x=4
y=61
400
If the equation for an exponential function is y=4 (5x), predict what the function will be at x=2.
y=100
400
Determine if this data belongs to a function that is linear, quadratic or exponential.
Exponential because the ratios are the same.
400
f(x) = -x2 + 6x - 8
What is the average rate of change of f(x) from [2, 3]?
A) -1/2 B) 1
C) -1 D) 1/2
B) 1
500
Determine if this graph has a positive, negative, or zero rate of change?
Positive
500
Which function is a quadratic?
F(x) is a quadratic
500
Which of the following IS an example of an exponential model?
A) f(x) = 3(2)x-2 B) g(x) = -4(x-2)2
C) h(x) = 3(2x-1) D) j(x) = 3x2 + 4x
A) f(x) = 3(2)x-2
500
Determine if this data belongs to a function that is linear, quadratic or exponential.
___x______y____
0 3000
1 2950
2 2900
3 2850
4 2800
Linear because the rate of change is constant
500
What is the average rate of change from x = -1 and x = 0?
AROC = -2