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### Course: Get ready for AP® Calculus > Unit 1

Lesson 2: Inputs and outputs of a function# Worked example: matching an input to a function's output (graph)

Sal finds the input value for which g(x)=-2 given the graph of g.

## Want to join the conversation?

- what is the purpose of functions exactly? They seem to remind me of how computers work (inputs and outputs). What word problems would functions be used as a solution? What problems in the world would need functions to find the answer? What are functions destined for? Thank you for answering!(25 votes)
- This is a fantastic question! Functions are used in computer science as you mentioned, although they don't follow the same definition that we use in algebra. Algebraic functions can be extremely useful for scientists, engineers, architects, you name it! For example, let's say that I am a botanist trying to determine the ideal amount of sunlight to expose a new species of plant to. I would conduct an experiment exposing plants to different amounts of light and record how tall they grew in each condition. Once I collect that data, I can use a function to model the pattern. This way I can predict the height of the plant under any light conditions. H would be height of the plant, and "t" would be amount of time exposed to the sun, so H(t) would be my function.(27 votes)

- How does Sal know that g(x)=y? what is the process to determine that?(12 votes)
- Technically, the blue line in the diagram should be tagged "𝑦 = 𝑔(𝑥)", and not just "𝑔(𝑥)".

However, the problem states: "The graph of the function 𝑔 is shown below.", which, by convention, implies that 𝑦 = 𝑔(𝑥).(9 votes)

- Hypothetically, if the question had been "What is the input value for which g(x) = 1?", given the same function in the video, what would be the correct way to answer this problem?

You've got g(x) = 1 for the inputs -6, 2, 1.5, 3, 5, and 7 through 8.

Would you just list them all, and is there a convention for this?(4 votes)- Take a look at the next video. They answer this question there :)(6 votes)

- I don’t understand. Why is it -9.(4 votes)
- g(x) is functional notation for a y =, so the question that is being asked if you have g(x) = - 2 is if y = -2 (same as g(x) = 2), what is the value of x? So if you find y = -2 by going down 2, you go across to an x value of - 9 .

If you wanted to find g(5), you would go across to where x = 5 and find the value of y.(2 votes)

- what about when you get What is the input value other than −2 for which h(x)=h(−2)?(4 votes)
- Find h(-2).

Look for another lattice point with the same y-value.

Look at the x-axis for the x-value.

Enter that in.(0 votes)

- What if the asked us g(x)=-1? There is two x values that if put in the function of g, get -1, what would be the answer here??(2 votes)
- @
**sharkel15**if you get only 1 y for every x then it is a function. Actually speaking the graph is plotted wrong but we may never know what the function is(2 votes)

- Is it possible to determine what the function is, just by looking at the graph?(2 votes)
- if you mean without writing down your work

it is in theory possible but it would be pretty hard to do mentally(2 votes)

- Can someone explain to me how to differentiate the when the question asks for the output or the input? A simple example will suffice(1 vote)
- When a question is asking for an input, it's asking for the x value that you plug into the function to get a specific y value, and when it's asking for an output, it's asking what y value you get when you plug in a specific x value. For example, if you're asked for an input for which a function equals 3, you would look for the x value on the function that has a y value of 3. Likewise, if you were asked for an output where x=3 you would answer with the function's y-value when the x value is 3.

Hopefully this helps.(4 votes)

- Why does g of X=y?(2 votes)
- The g of x is replaced any f of x and f of x just means the X symbol is what ever is in the () and the F is all left and according to any function like quadratic any leter on the outside and isolated equals Y(1 vote)

- What is the answer if the y coordinate crosses x axis at 0?(2 votes)
- If the y intercept of a linear function is zero, then the equation is a direct proportion and the line would go through the origin (0,0), it would be in the form of y = kx where k is the constant of proportionality.(1 vote)

## Video transcript

The graph of the function g is shown below What is the input value for which g of x is equal to negative 2? So what they do here is along the x axis these are the inputs and then the graph shows us what's the output so when x is equal to 7, G of 7 we see here is 1. If x equals 9, g of 9 here is 2. If x equals 6, g of 6 is equal to the y coordinate at this point is equal to 0. so what is the input value for which g is equal to negative 2? so this graph over here, this is y equals g of x. So g of x equaling to negative 2 means y of x is equal to negative 2 And so when does y equal negative 2? (muttering) when does equal negative 2? (talking) it looks like that happens right at this point. And that happens when you input negative 9 into g. g of negative 9 is negative 2 so this is going to be negative 9. And we're done.