Function Notation
Function Representations
X & Y
Intercepts
Intercepts
Domain & Range
Key Characteristics of Graphs
100
f(x) = 3x - 7
Find f(4)
3(4) - 7
12 - 7
5
100
Is this relation a function? Why or why not?
Yes - every x-value/input has exactly one y-value.
100
Identify the y-intercept(s):
(0, -3)
100
What is the domain of the relation?
{-10, 0, 3, 7, 8}
100
Is the function discrete or continuous?
This function is DISCRETE since it is made up of dots.
200
find f(8)
f(x) = 1/2 x + 2
1/2 (8) + 2
4 + 2
6
200
Does this graph represent a function? Why/Why Not?
No - it does not pass the vertical line test.
No - there are two y-values for the same x-value.
200
Identify the x intercept(s):
(-4, 0) and (2, 0)
200
What is the range of the relation?
{-8, -4, 2, 3, 6}
200
Identify if the function is...
Linear or Nonlinear
A function or Not a function
Continuous or Discrete
Nonlinear, Not a function, continuous
300
f(x) = -4x + 8
Find x if f(x) = 20
-4x + 8 = 20
x = -3 if f(x) = 20
300
Write the mapping as a list of ordered pairs. Is it a function YES or NO?
(0,7), (0, 16), (1, 10), (20, 16)
NO - the x-value of 0 has two y-values of 7 and 16.
300
Jolene goes to costco for gas. The x-axis represents the amount of gallons she's put into her tank and the y-axis represents how much money she's spent.
What does the x-intercept mean IN THIS SITUATION?
The x-intercept, (0,0) means that 0 gallons of gas costs her $0.
300
What is the Domain of the function?
{-3, -2, 3, 5}
300
Use the graph to identify the relative minimum(s) and maximum(s)
Relative Minimum: (4, -8)
Relative Maximum: (0,0)
400
A car rental company charges a base fee of $25 and $1 per mile driven. The function C(m) = 25 + 1m is used to calculate the total cost of renting the car.
Find C(150). What does it represent?
C(150) = $175 and represents the total cost if someone drives the car 150 miles.
400
Express the relation below as a mapping and a graph. Is it a function YES or NO?
It is NOT a function because the x-value, 12, has two y-values, -4 and -7.
400
Indira is mountain climbing and starts the day at 182.5 meters above sea level. Each hour she descends 36.5 meters. The table shows the function relating Indira's height to the number of hours she is mountain climbing.
Find the x-intercept and interpret it in the context of the problem.
The x-intercept is (5, 0), which means that it will take 5 hours for Indira to reach the bottom of the mountain.
400
What is the Range of the function?
{5, 4, 0, -3}
400
Use the graph to identify when the graph is increasing and when the graph is decreasing:
Increasing: x > -1 (x is greater than negative 1)
Decreasing: x < -1 (x is less than negative 1)
500
Luke is driving home from work. D(t) calculates Luke's remaining distance to drive after t minutes of driving. What does the statement D(0) = 10 represent?
D(0) = 10 represents the fact that if Luke hasn't spent any time driving, he still has 10 miles until he is home.
500
Draw a graph, either discrete or continuous, that is NOT a function.
All answers will FAIL the vertical line test.
A discrete graph will have various points with at least two points directly above/below each other.
A continuous graph will have a curve with some part directly above/below another section of the graph.
500
Interpret the x-intercept (18,0) and the y-intercept (0,360) for this situation.
(18,0) means after 18 minutes the hiking elevation is 0 feet above the canyon.
(0, 360) means at the start of the hike they were 360 feet above the canyon.
500
List 2 numbers in the domain and 2 numbers in the range using the graph:
Possible Numbers:
Domain: x > 3 (any x-values greater than 3)
Range: y < 5 (any y-values less than 5)
500
Use the graph to identify the end behavior:
Left side of graph: As x decreases, y ... increases!
Right side of graph: As x increases, y ... increases!