Worked example: matching an input to a function's output (graph)
About this video
Using the graph of a function g, the video explains that inputs are on the x-axis and outputs are the y-values, reading g(7) = 1, g(9) = 2 and g(6) = 0. It then finds the input for which g(x) = -2 by looking for where the graph has a y-value of -2, which is at x = -9.
You'll be able to
- read inputs and outputs from the graph of a function.
- find the input that gives a particular output by reading across a graph.
Key words
- input
- The x-value, read along the horizontal axis.
- output
- The y-value of the graph at a given input, written g(x).
- y = g(x)
- The graph shows every point where the y-coordinate equals g of the x-coordinate.
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.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.