Today we're going to talk about evaluating functions. So we'll look at examples evaluating functions algebraically using something called function notation. And we'll also do an example evaluating a function by looking at its graph.
So here's an example of a function f of x is equal to 3x squared minus 8. And this function 3x squared minus 8, or f of x, is a function of x, where x is referred to as the input, or the argument of the function. And the value of the function depends on the value of the input or the argument.
So let me give you an example. Depending on which value I pick for my input, my value for x, I will have a different value of my function. So for example, let's say I pick the input value of 3. I'm replacing three with x in my function notation.
So I'm going to also replace every x that I have with a value of 3. So now my function becomes 3 times 3 squared minus 8. I can simplify this to become 3 squared, which is 9.
So 3 times 9 minus 8. 3 times 9 is going to give me 27. And 27 minus 8 is going to give me 19. So I found that f of 3 is equal to 19, or the value of my function is 19 when my input is 3.
I can do another example with a different input value. And we can determine what the value of my function is. So here I'm replacing my value for x with negative 1. So my input value is negative 1. I'm Going to replace every instance of x in my function with negative 1.
So this will become 3 times negative 1 squared minus 8. Simplifying this, negative 1 squared is positive 1. 3 times 1 will give me 3. And 3 minus 8 is negative 5. So I found that f of negative 1 is negative 5. Or my value of my function is negative 5 when my input value is negative 1.
So let's see how we can evaluate a function by looking at its graph. I have the function f of x equals 2x plus 1 and its corresponding graph. Let's say I wanted to find f of 2, or the value of the function when x, the input value, is 2.
So I know that I can find that by substituting 2 for my x value. And that would give me 2 times 2, which is 4 plus 1. So that would be 5. So I know that f of 2 is equal to 5 by looking at this equation in function notation.
I can also find the value of the function at the input value of 2 by finding 2 on my x-axis, and then going up or down to my graph, and then going over to the y-axis to look for the corresponding y value, which is the value of the function. So I can also see that when my input value is 2, the value of my function is 5.
So finally, let's look at one other example of evaluating the function using function notation. So let's say I have the function f of x is equal to negative 2x minus 4. So I know the function, f of x, is equal to negative 2x minus 4. I want to find f of x plus 5.
So similarly to evaluating a function when our input value is numerical, I'm going to replace this in my parentheses, this expression in my parentheses, into my original equation or my function for every instance of x. So here I have x, I'm going to replace it with my x plus 5.
So this is going to become negative 2 times, instead of x, I'm going to replace it with x plus 5. And then I'll bring down my minus 4. Now to finish evaluating, I can simplify this expression. I'm going to start by distributing this negative 2.
Negative 2 times x would give me negative 2x. Negative 2 times 5 will give me plus a negative 10, bring down my minus 4. I can combine these two constant terms. Negative 10 minus 4 is going to give me negative 14.
So this becomes plus negative 14, which is to say as minus 14. So I found that f of x plus 5 is equal to negative 2x minus 14.
So let's go over our key points from today. f of x is a function of x, where x is referred to as the argument. The argument of the function is the input value on which the value of the function depends. You can evaluate a function algebraically by substituting a given value in the domain for x. And you can evaluate a function graphically by finding a given value in the domain on the x-axis and determining the corresponding y value of the function.
So I hope that these key points and examples helped you understand a little bit more about evaluating functions. Keep using your notes and keep on practicing, and soon you'll be a pro. Thanks for watching.