Kinds of Functions
In a function, how many outputs should each input have?
No more than 1
If the rule of a function is "add 3, then multiply by 2," what would the output be for an input of 4?
14
Write an equation in slope-intercept form for a line with a y-intercept of 2 and a slope of 3.
y = 3x + 2
Solve the following equation:
x + 5 = -2
x = -7
Input Output
4 7
2 -3
4 2
No, the input of 4 produces 2 different outputs (7 and 2).
If the rule of a function is "divide by 3, then add 5," what would the output be for an input of 18?
11
Write an equation in slope-intercept form for a line with a y-intercept of -6 and a slope of 2.
y = 2x - 6
Solve the following equation:
3x - 6 = 0
x = 2
Does the following table show a linear or non-linear relationship?
Input Output
-2 7
-1 4
0 9
1 2
Non-linear
Fill in the blanks for the following input/output table?
Input Output
1 7
5 11
-2 ___
___ 19
Input Output
1 7
5 11
-2 4
13 19
The equation for a horizontal line that crosses through point (6,-28)
y = -28
Solve the following equation:
3x + 2x - 5 = 15
x = 4
Does the following table show a linear or non-linear relationship?
Input Output
-2 -1
-1 1
0 3
1 5
Linear
The table below shows the temperature in a city in x hours after 12:00 PM. When was the temperature the highest?
Hours Temp (F)
0 73
4 68
1 76
3 75
2 71
1:00 PM
The equation of a vertical line passing through the point (5, -8).
x = 5
Solve the following variable for y (y should be by itself):
5x + y = -3
y = -5x - 3
OR
y = -3 - 5x
The following table shows a car's distance from home and the amount of time it has been driving. Was the car driving at a constant speed? Why?
Time (hours) Distance (miles)
0 0
1 45
2 90
3 120
No, the car went 45 miles per hour for the first 2 hours, then slowed to 30 miles per hour (or similar explanation)
What is the rule for the following function?
Input Output
1 7
2 9
3 11
4 13
5 15
Multiply by 2, then add 5.
To open a cellular plan, AT&T charges you 40 dollars per month along with a one-time 70 dollar fee to start service. Write a function (equation) that demonstrates how much you would get charged for x months of service.
y = 40x + 70
Solve the following variable for y (y should be by itself):
-4x + 2y = 12
y = 2x + 6