Graph Transformations
Domain and Range
Interpretation
Composite Functions
Test Your Knowledge
100
If (2, 3) is on the graph of y = f(x), what are the new coordinates if y = f(x + 1) + 3?
(1, 6)
100
Which of the following parent functions is decreasing over its entire domain?
A) y = 1/x
B) y = x3
C) y = |x|
D) y = x
A) y = 1/x
100
Ellie manages her mom's online candle business, Cathy's Candles, and is responsible for setting prices that will maximize revenue, R. The equation
R(c) = (500-5c)(c-4)
models the total revenue earned when c dollars is charged for one candle.
Find R(7) and interpret the value in the context of the problem.
$1395.00
She will make $1395 if she sells candles for $7.00 each.
100
The graph of y = g(x) is shown. Find g(-3)
3
100
What is the parent function?
absolute value
200
What are the following transformations?
g(x) = - f(x+2)
reflection over the x axis and 2 units left
200
The term used for the set of all possible input values
Domain
200
Let M(t) represent the rate at which people enter Macy's department store, in people per hour, t hours into their Black Friday sale. interpret the statement M(3.5) = 432 in the context of the problem.
3.5 hours after opening, there will be 432 people in the store.
200
f(x) = |x| is shown below and g(x) is shown below.
what is f(g(-1)
0
200
What is the range of the function?
[-1, +∞)
300
The graph of
f(6x)
represents what kind of transformation?
Horizontal shrink
300
What is the range of the following function:
[1, 5]
300
Let n(t) represent the tailwind of an airplane, in miles per hour, t hours into the flight. using correct units, interpret the statement
n(3.5) = 67
in the context of this problem.
After 3.5 hours into the flight, the tailwind is 67 miles per hour.
300
Given the definitions of f(x) and g(x) below, find the value of g(f(0)).
f(x) = 3x2+ x - 6
g(x) = -4x - 3
21
300
What is the identity function?
y = x
linear
400
Identify the parent function and then the transformation that occured from the parent function to produce:
f(x) = -(x+2)3
Cubic = x3
Horizontal shift left 2
Reflections about x-axis
400
What is the domain of the following function:
[1, 4]
400
A Fed Ex driver is delivering packages ordered from Amazon. The function P(t) represents the rate, in packages per hour, that the driver is delivering packages, where t is measured in hours. Using correct units, interpret the meaning of the following in context of this situation:
P(2)= P(5)
At 2 hours and 5 hours the delivery driver delivers the same amount of packages an hour.
400
A table of selected values is given for functions f and g. The domain of both functions is all real numbers
Find f(g(1))
x | f(x) x | g(x)
-2 |-1 -2 | 6
-1 | 1 -1 | 4
0 | 3 1 | 0
1 | 4 2 | -2
2 | 7
3
400
What are the transformations to the graph compared to the parent function?
Shifted right 2, shifted up 3, and reflected over the x-axis
500
How is the graph of f transformed to create the graph of g?
f(x) = x^2
g(x) = 3f(x) - 4
vertically stretched by a factor of 3, translated down 4
500
Which set of ordered pairs is not a function?
A. (1, 3), (2, 7), (3, 8), (4, 11)
B. (2, 3), (4, 9), (3, 8), (4, 15)
C. (1, 2), (3, 5), (6, 9), (7, 11)
D. (-9, 4), (-6, 3), (-2, 8), (0, 21)
B. (2, 3), (4, 9), (3, 8), (4, 15)
500
A Fed Ex driver is delivering packages ordered from Amazon. The function P(t) represents the rate, in packages per hour, that the driver is delivering packages, where t is measured in hours. Using correct units, interpret the meaning of the following in context of this situation:
P(K)= 34
At some time K, the deliver driver delivers 34 packages an hour.
500
A table of selected values is given for functions f and g. The domain of both functions is all real numbers
Find g(f(-2))
x | f(x) x | g(x)
-2 |-1 -2 | 6
-1 | 1 -1 | 4
0 | 3 1 | 0
1 | 4 2 | -2
2 | 7
What is the average rate of change of
f(x)= x2+4x+4 from x=1 to x=-3
4
500
f(x) = −(x+2)3−1