3 Vocabulary Terms - Define/Illustrate
Domain
Range
End Behavior of a Linear function
5 Problems - SHOW ALL WORK!
Write a function that describes the cost to have your vehicle towed if you are charged $15 for the pickup plus $2 for every mile.
The cost of a gym membership if there is a $50 enrollment fee and the charge is $35 a month.
Use the following functions to solve each:
f(x)= 2x - 3 g(x)= -4x -1
What is f(3)?
Which function has a steeper slope?
Use the following functions to solve each:
f(x) = 2x -3 4x - 7y = 28
Which function has the greater y-intercept?
What is f(-2)?
Does the table or the graph represent a steeper slope?
Does the table or the graph have a bigger y-intercept?
What do I need help with?
Domain: The set of all possible input values of a function. It is the independent variable in a relation.
Range: The set of all possible output values of a function. It is the dependent variable in a relation.
End Behavior of a Linear Function: The behavior or tendency of the graph of a linear function as the input values approach positive and negative infinity. It can be determined by looking at the slope of the linear function.
1) Function for the cost of vehicle towing:
Let x be the number of miles.
The cost to have your vehicle towed = 15 + 2x.
2) Function for the cost of a gym membership:
Let x be the number of months.
The cost of a gym membership = 50 + 35x.
3) f(3):
Plug in x = 3 into f(x) = 2x - 3.
f(3) = 2(3) - 3
f(3) = 6 - 3
f(3) = 3
4) Steeper slope:
To determine the slope, we look at the coefficient of x.
Slope of f(x) = 2
Slope of g(x) = -4
Function f(x) has a steeper slope.
5) Greater y-intercept:
To determine the y-intercept, we look at the constant term.
Y-intercept of f(x) = -3
For 4x - 7y = 28, rearrange the equation to solve for y.
-7y = -4x + 28
Divide by -7 on both sides to get the coefficient of y to be positive.
y = (4/7)x - 4
The y-intercept of the second function is -4.
Function f(x) has the greater y-intercept.
6) f(-2):
Plug in x = -2 into f(x) = 2x - 3.
f(-2) = 2(-2) - 3
f(-2) = -4 - 3
f(-2) = -7
7) Table or graph with steeper slope:
To determine the slope, we can compare the change in y-values to the change in x-values.
If the change in y-values is greater compared to the change in x-values, then the slope is steeper.
If the table shows bigger differences in the y-values compared to the x-values, then the table represents a steeper slope.
8) Table or graph with bigger y-intercept:
To determine the y-intercept, we can compare the y-value when x = 0.
If the y-value is greater in the table compared to the graph, then the table has a bigger y-intercept.
If you need help with anything specific, please specify the topic or concept.