Inputs vs. Outputs
The concept of Inputs and Outputs can be confusing at first, but we promise it gets easier! We’ve broken down each to help you see how they’re connected!
Inputs
The input is what you need to know before finding the function’s output, or outcome. When you have a function, the input is what goes into it. Inputs are commonly represented as “x”, but they could also be represented with other variables. An input is also known as an independent variable.
The last example (the one using g(m) in the function) shows how f(x) doesn’t always have to use the variables “f” and “x”. Instead of “f”, we used “g”. Instead of “x”, we used “m”.
Your turn!
Can you find the input?
Problem 1
g(2) = 53/2
Ready for the answer?
The input is 2! This is because in "g(2)", there's a "2" in the parenthesis. This shows us what the input is because the number/variable in the parenthesis is our input.
Problem 2
d(s) = 3s - s
Ready for the answer?
The input is s! This is because in "d(s)", there's an "s" in the parenthesis. This shows us what the input is because the number/variable in the parenthesis is our input.
Outputs
The output is information you figure out using a given input. When you have a function, the output is what comes out of it, or the result. In a function, the output is usually represented with “f(x)” where x is the input. In equations, outputs are commonly represented as “y”, but they could also be represented with other variables. An output is also known as the dependent variable.
If you had trouble with any of these, make sure to refresh your memory on Exponent Rules!
Your Turn!
Can you find the output using the function f(x) = 4x+2?
Problem 1
x = 5
Ready for the answer?
The output is 22!
Steps:
1. f(x) = 4x+2
2. f(5) = 4(5)+2
3. f(5) = 20+2
4. f(5) = 22
Problem 2
x = -3
Ready for the answer?
The output is -10!
Steps:
1. f(x) = 4x+2
2. f(-3) = 4(-3)+2
3. f(-3) = -12+2
4. f(-3) = -10
Problem 3
x = 1/2
Ready for the answer?
The output is 4!
Steps:
1. f(x) = 4x+2
2. f(1/2) = 4(1/2)+2
3. f(1/2) = 2+2
4. f(1/2) = 4
Tables
Let's learn how to identify your independent and dependent variables on a table! Most of the time, you can tell which is what by looking at the data. Let’s look at an example!
Here’s how much homework each student is assigned every week:
The input is the number of weeks and the output is the hours worth of homework. This is true because the hours of homework each student is assigned depends on how many weeks it’s been. When the number of weeks increases, so does the hours of homework.
Your Turn!
Problem 1
Mia is selling apples, the revenue is listed in the table below:
Can you figure out what the inputs and outputs are?
Here’s the answer!
The table shows us the revenue based on how many apples a customer was to buy. This means the inputs are the number of apples and the outputs include the generated revenue from the apples. This is true because the gain depends on how many apples Mia's customers are buying. When the number of apples increases, the revenue does too.
Problem 2
Matthew throws a ball, here’s a table to model the ball’s path:
Can you figure out what the inputs and outputs are?
Here’s the answer!
The table shows us the height of the ball based on how long it's been since Matthew threw the ball. This means the input's the time and the output's the height of the ball. This is true because the height depends on time.
Graphs
Now let’s dive into how to find the inputs and outputs of a graph! The input is usually the x value of a coordinate and along the horizontal axis of a graph. The output is usually the y value of a coordinate and along the vertical axis of a graph.
Example: If we look at the coordinates (2, 3), you can tell that 2 is the input and 3 is the output. A coordinate is (x, y), and since we know 2 equals x, we know 2 is the input. You can tell that 3 is the output because we know 3 equals y.
Your Turn!
Figure out the input and output from the following coordinates:
Problem 1
(-4, 1)
Ready for the answer?
Input: -4
Output: 1
Problem 2
(1/5, 90)
Ready for the answer?
Input: 1/5
Output: 90
Final Thoughts
Outputs depend on inputs, and now that you’ve learned the difference between the two, make sure to read some of our other posts!
Still need help? Get in touch with a UPchieve tutor to work with you for free.