Worked example: evaluating expressions with function notation
About this video
The video evaluates -2 times f(-6) plus g(1) using graphs of f and g. It reads f(-6) = 7 and g(1) = -5 from the graphs, substitutes them, and simplifies -2(7) + (-5) to get -19.
You'll be able to
- read function values like f(-6) from a graph.
- substitute function values into an expression and simplify it.
Key words
- evaluate
- Work out the value of an expression.
- input
- The x-value you put into a function, read along the horizontal axis.
- function notation
- f(-6) means the output of function f when the input is -6.
Transcript
We're asked to evaluate negative 2 times f of negative 6 plus g of 1. And they've defined, at least graphically, f of x and g of x here below. So let's see how we can evaluate this. Well, to do this, we first have to figure out what f of negative 6 is. So our input into our function is negative 6.
And we'll assume that's along the horizontal axis. So our input is negative 6. And based on our function definition, f of negative 6 is 7. So this thing. Let me write this down. f of negative 6 is equal to 7. And what is g of 1? Well, once again, here's our input axis.
And then the function says that g of 1, which is right over there, is negative 5. g of 1 is equal to negative 5. So this statement simplifies to negative 2 times f of negative 6, which is 7. So times 7 plus g of 1, which is negative 5. So plus negative 5, which simplifies to-- let's see.
Negative 2 times 7 is negative 14 plus negative 5, which is negative 19. And we are done.
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