Determine whether the following is an example of a function. Explain why or why not.
x - The people in this classroom
f(x) - The types of shoes they are wearing.
Yes... Unless there is a person wearing two different shoes...
100
What is the domain and range of the function represented by the following ordered pairs?
(2, -3), (4, 5), (6, 0), (7, 3)
Domain: 2, 4, 6, 7
Range: -3, 5, 0, 3
100
Graph the parent function:
f(x) = 1/x
Figure D
100
If f(x) = 3x2+1,
what is f(7)?
148
100
Refer to Figure A.
Give the intervals where it is...
- increasing
- decreasing
- constant
EZ has a dog walking business where his net profit (P), of walking (d) amount of dogs is given by the function below:
P(d)= 20d - 20. If EZ walks 5 dogs, what is his net profit?
$80
200
Give the domain and range of the parent function f(x) = abs(x) in interval notation.
If you were to graph the function
f(x) = 2x + 1
What is the parent function?
How did this function change from the parent function?
- Identity Function or Linear
- It is steeper and has shifted up 1 unit
200
Refer to figure A.
Find f(-5)
f(-5) = 4
200
Refer to figure F.
Which graph could represent the height of a human as a function of time?
B
300
Explain the difference between f(x) and -f(x).
-f(x) is reflected over the x-axis
OR All of f(x)'s y's have changed signs.
e.g. -2 becomes 2
300
Refer to figure A.
State its Domain and Range in interval and standard notation.
Domain: [-5, infinity)
Range: [1, infinity)
300
Refer to figure B.
Write an equation for the function of this graph.
f(x) = abs(x-3) + 2
300
If f(x) = 2x and g(x) = 3x + 1
Find (f - g)(3)
-4
300
Suppose that the x-intercepts of a function f(x) are -2 and 5. Then the x-intercepts of the graph of f(x + 1) are _____ and _____.
-3 and 4
400
A hamster is thrown vertically upward. Its height in feet (h) after (t) seconds is given by the function below:
h(t) = 64t - 16t^2
After how long will the hamster reach its maximum height?
(no hamsters were harmed in the making of this math problem)
2 seconds
... @ a height of 64 feet
400
A function has a domain represented by (3, infinity) and a range of (-2, 6].
Give the function's domain and range in standard notation.
Domain: x > 3
Range: -2 < y < 6 (second "<" is underlined)
400
Graph the function:
f(x) = - sqrt(x - 2)
Figure C
400
Refer to figure A.
What is the rate of change from -2 to 4?
Using pts (-2, 1), (4, 4)
Rate of Change = 1/2
400
Refer to figure G.
Is there a relative Minima or Maxima?
If so, where?
Min @ (-4, 2)
Max @ (-3, 4)
500
Mady is building a pen for her llama. She wants to maximize the area of the pen for the materials that she has.
The area of the pen (A), in feet, is given below as a function of the width of the pen (x).
A(x) = -2x^2 + 50x
If the length of the pen is twice the width, what is the length of the pen when its area is at its maximum?
25 feet
500
Give the Domain and Range of the function
f(x) = - (x)2 +2