Functions
Graphing Functions
Transforming Functions
Evaluating Functions
Characteristics of Functions
100
Is this graph a function?
Function
100
Is the function linear or nonlinear?
f(x) = 1/x
Nonlinear
100
g(x) is the transformation of
f(x) = x^2
What is the function g(x) represented by the graph?
g(x) = (x-3)^2
100
f(x) = 3x - 7
f(-2) =
-13
100
The domain of a function are the _______________ values of the function.
input or x
200
Is this table a function?
Yes
200
Is the function linear or nonlinear?
f(x) = 3x + 7
Linear
200
What is the effect on the graph of
f(x) = 1/x
when it is transformed to
h(x) = 1/x +6
The graph of f(x) is shifted up 6 units
200
f(x) {3x+1 if x > 0
{ x-5 if x < 0
Evaluate the function when f(-10)
f(-10) = -15
200
A function is positive when it is ________________.
above the x axis.
300
Raquel is a member of an online book library that charges $1.50 per book. The cost, C(b), is represented by C(b) = 1.50b, where b is the number of books Raquel borrows.
Identify the independent variable.
b, the number of books Raquel borrows
300
Where is the function below negative?
f(x) = |x|
Never
300
g(x) is a transformation of f(x) = |x|. What is the function g(x) represented by the graph? 
g(x) = -|x| + 5
300
f(x) = (1/2)x - 7
f(12) =
f(12) = -1
300
The range of a function are the _______________ values of the function.
output or y
400
Identify the domain and range
Domain: All real numbers
Range:
y<=3
400
What is the parent function of this graph? 
f(x) = x
400
What are the effects on the graph of
f(x) = root3 x
when it is transformed to
f(x) = root3 (1/3x) -8
?
The graph of f(x) is stretched horizontally by a factor of 3 and shifted down 8 units
400
Find (f - g)(x)
f(x) = 5x^3 +8x^2-7x-3
g(x) = 2x^2 -5x - 10
(f-g)(x) = 5x^3 +6x^2 -2x + 7
400
A function is decreasing when it is moving __________ as it moves ______________.
down; right
500
Identify the domain and range
Domain
2<=x<=6
Range
6<=y<=18
500
Where is the function below decreasing?
f(x) = 6x + 8
Never
500
In the following function, how do a, h, and k transform the graph?
a f(x) = x - h + k
a: determines the vertical shrink or stretch
h: determines the shift to the left or right
k: determines the shift up or down
500
A building materials company sells gravel. Suppose that
C(x) = 0.5x^2 +3x
represents its estimated monthly cost, and
R(x) = -0.002x^3 +5x^2-10x
represents its estimated monthly revenue, where x is in thousands of pounds of gravel sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?
P(x) = -0.002x^3+4.5x^2 -13x
500
What is the end behavior of a linear function with a positive slope?
As x reaches positive infinity, y reaches positive infinity. As x reaches negative infinity, y reaches negative infinity.