Input and Output Values: How to find Inputs and Outputs on a Graph

(Ignore the answer put into the box, this was when I first was inputs and outputs, and I was totally wrong 😀 )

At first glance, you may think this seems very complicated, right? Actually, this is a very easy thing to understand. Today, I will be showing you how to indicate inputs and outputs on a graph! 😀

At you can see this equation is quite long. To make things more simple, let’s remove some properties.

Our new equation: f(-8) x g(4)=?

To first solve this, we must know what a input and output is. A input is something that is put in. For example, when ordering groceries, your input would be your money. A output is a result of a input. Since your input is the money, your output would be your groceries. It is almost like a cause and effect, but in math terms!

Now that we know that an input and output is, lets look at the picture. There are two crooked lines: one in red and the other in blue. The red has a equation of y=g(x) and the blue has an equation of y=f(x). You may be wondering, what does this mean?

Let’s start with y=g(x), the red line equation, and the original equation we are trying to solve for. f(-8) x g(4). As you can see, the two problems have a difference: the x is substituted for 4. So, what happened to the variable? X stands for the x-coordinate and g stands for the output. Since x is 4 and g is not included, this indicates that the person wants us to find g.

To find g, we can look at the the graph and look for a 4 on the x-axis. If you put your finger the four and slide up to where the line is, you should get 3. So this means for g(4)=3.

Reminder: Usually when we see a number next to a parenthesis, we multiply. But since we are dealing with outputs and inputs, the values are not multiplied and instead are simply the output.

Now that we have found/ the value of g(4), we can substitute it into our equation.

New equation: f(-8) x 3=

Now to find f(-8), we will do the same thing, Remember, the blue line equation is y= f(x). So, -8 is going to be the x-coordinate.

If you place your hand on -8 on the x-axis and slide up, you should get the answer 2. Now that we have the answer to f(-8), let’s add it into the equation and solve!

Simplified equation: 2 x 3

Two times three equals six, so our answer is six!

Good job learning how to identify outputs and inputs! If you do not understand something, tell me in the comments so that I can write some simpler problems for you to understand. Have a good day!