Function Vocabulary
What is the definition of a function?
Every input has ONE and ONLY ONE output.
{(3,4),(4,5),(7,12),(3,6)}
No, the input of 3 has two outputs (4 and 6).
Draw the general form for function notation.
f(x)=y
Name a common rate we see in our everyday life.
miles per hour (mph)
(other answers accepted by teacher)
The point where a line crosses the Y-axis.
Vertical intercept
The x value is called the ______
Input
The relationship between the amount of time a car is parked, in hours, and the cost c of parking, in dollars, can be described with a function. Identify the independent variable and the dependent variable in this function.
independent: hours
dependent: cost
Function C takes time for its input and gives a student’s Monday class for its output. Use function notation to represent: A student has English at 10:00.
C(10:00) = English
When the independent variable increases and the dependent variable also increases, the rate of change is _____ (+ or -)
positive
The point where a line crosses the X-axis.
Horizontal intercept
The y value is called the ________
Output
The relationship between the amount of time a car is parked, in hours, and the cost of parking, in dollars, can be described with a function. Describe the function with a sentence of the form "____ is a function of ____."
The parking cost is a function of the amount of time a car is parked.
Solve the following:
f(x)=3x+5
when x=4
17
A climber is taking a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What was his average rate of change over those 4 hours?
75 feet per hour
The rate of change of a line is called the ____.
slope
When a function increases or decreases at a constant rate. When graphed, it will form a continuous straight line.
Nicole charges a flat rate of $6 and an additional $4 per hour of babysitting. Write a function that gives the total cost, C, of babysitting for h hours.
C(h)=4h+6
Function P gives the perimeter of an equilateral triangle of side length s. It is represented by the equation P(s)=3s
1. The perimeter of an equilateral triangle of side length s is 60.
2. s=20
A teacher weighed 150 lbs in 1986 and weighs 190 lbs in 2006. What was the average rate of change in weight?
2 pounds per year
The highest point that a line reaches on a graph.
Maximum
Define independent and dependent variables.
Independent variable is the INPUT, and the dependent variable DEPENDS on the independent variable.
Attorney A charges a fixed fee of $250 for an initial meeting and $150 per hour for all hours worked after that. Attorney B charges $150 for the initial meeting and $175 per hour. Write TWO functions A and B that represent the cost of each attorney per hour. Which attorney has the better cost for 25 hours of work?
A(x)=150x+250
B(x)=175x+150
Attorney A has the better cost for 25 hours.
Function f is defined by the equation f(x)=x2.
What is f(2)+f(3)
13
A plane left Chicago at 8:00 A.M. At 1:00 P.M., the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip?
300 miles per hour
This test will show if a graph is a function or not.
The Vertical Line Test.