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
Does the graph have a line of symmetry? If yes, what is the equation of the line. If no, why not?
YES. X = 0
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
Use the graph to identify the relative minimum(s) and maximum(s)
Relative Minimum: (0, 0)
Relative Maximums: (-2, 16) and (2, 16)
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
Use the graph to identify when the graph is increasing and when the graph is decreasing:
Increasing: x > -1
Decreasing: x < -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
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
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!