Function Notation
Function Representations
X & Y
Intercepts
Intercepts
Domain & Range
Grab Bag
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
Determine the Independent and Dependent quantities using the graph.
Independent: Ticket Price
Dependent: Attendance
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
Continous 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
Nataliah can read 160 words per minute. Let w represent the total number of words Nataliah reads, and let m represent the number of minutes she spends reading.
Identify the Independent and Dependent Quantities:
Independent: # of Minutes Read
Dependent: # of Words Read
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.
What does c(150) represent?
c(150) represents the total cost if someone drives the car 150 miles.
400
Express the relation below as a table, 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
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.
400
What is the Range of the function?
{5, 4, 0, -3}
400
What does the origin (0, 0) represent in this situation.
Leona earns zero dollars if she delivers zero newspapers.
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
Sketch non-linear, continuous relation that is IS NOT a function AND Sketch a linear, discrete relation that IS a function.
Examples:
Non-linear, continuous, NOT a function:
Linear, Discrete, IS a function:
500
Calculate the x and y intercepts of the line
13x - 2y = -26
x-intercept: (___, 0)
y-intercept: (0, ___)
x-intercept: (-2, 0)
y-intercept: (0, 13)
500
List 2 numbers in the domain and 2 numbers in the range using the graph:
Possible Numbers:
Domain: x > 3
Range: y < 5
500
Charlie worked for a stone setting company this past summer. He earned $50 just for coming to work and an additional $30 every hour for each hour he worked. The linear function E(h) = 50 + 30h represents Charlie’s earnings.
What does E(h) = 230 represent?
Find what h =
E(h) = 230 represents that after h hours, Charlie makes $230.
h = 6
If Charlie wants to earn $230, he must work for 6 hours.