Functions
This is a relation where each input (x) has exactly one output (y).
A function.
What is the set of all possible values of x in a relation called?
The domain
This is the general form of a linear equation.
y=mx+b
To graph the line represented by the equation y=x+2, this point should be plotted first.
The y-intercept, (0, 2)
A line passes through the points (0,4) and (1,6). This is the equation for the line.
y=2x+4
If a set of ordered pairs is {(1, 3), (2, 4), (3, 4), (4, 6)}, is this relation a function?
Yes, this is a function because each input (x-value) has only one output (y-value).
The relation is represented by the set of points {(2, 3), (4, 5), (6, 7), (8, 9)}. What is the range of this relation?
{3, 5, 7, 9}
What is the slope of a line that passes through the points (1,2) and (3,6)?
2/1
The graph of the equation y=3x−4 will have a slope of this.
3
A store charges a fee of $5 plus $2 for each item purchased. This equation models the total cost y for purchasing x items
y=2x+5
What can a vertical line test tell you about a relation.
Whether the relation is a function
This set of ordered pairs is {(3, 2), (4, 3), (5, 4), (6, 5)}. What is the domain and range?
The domain is {3, 4, 5, 6} and range is {2, 3, 4, 5}
In the equation y=3x+4, the value of 4 represents what?
The y-intercept or starting point.
Given the equation y=−x+3, this point should be plotted on the graph first and then this will be the change made to that point each time.
The y-intercept, (0,3), with a slope of -1/1.
You are given the table of values: {(1, 3), (2, 6), (3, 9), (0,0)}. This is the linear equation that matches the table.
y=3x
{(1, 5), (2, 6), (3, 7), (4, 8), (1, 9)}
Is this relation a function? Why or why not?
No, because the input 1 is paired with two different outputs: 5 and 9.
What is the set of all possible values of y in a relation called?
The range
Given this equation of a line, y=−2x+5, what is the slope?
-2
Write the equation that represents a line with a slope of 1 and a y-intercept of -2.
y=x−2
A student’s score increases by 5 points each time they study for 30 minutes. The starting score is 50 points. Write the equation.
y=5x+50
A relation is represented by the set of points {(0, 2), (1, 4), (2, 6), (3, 8)}. Is this a function? What are the domain and range?
Yes, this is a function with a domain of {0, 1, 2, 3} and a range of {2, 4, 6, 8}
A relation is given by the set of points {(1, 2), (3, 4), (5, 6)}. What is the domain and range if the function continues with a pattern?
The domain is {all odd numbers} and the range is {all even numbers}
This characteristic of a linear function tells you how much the value of y changes for each unit increase in x.
The slope
If you are given a table where x=−2,−1,0,1,2 and the corresponding y-values are {4, 3, 2, 1, 0}, write the equation to graph this linear equation.
y=−x+2
The table shows the following values for x and y:
x=0,1,2,3,4 and y=10,12,14,16,18. What is the equation of the linear function that represents the situation?
y=2x+10