00:01
Given this piecewise function, f of x, let's evaluate the following.
00:05
First, we have f of negative 3.
00:08
Now, negative 3, the input value, is less than negative 1.
00:12
So we should be using the top rule here, the negative 2x squared plus 3.
00:19
So let me go ahead, instead of writing an x, we'll stick in a negative 3 there.
00:26
Notice how i wrote the negative 3 with a set of parentheses around it.
00:30
It's to emphasize that really this rule is telling me that i'm squaring the input first, and then i'm multiplying by negative 2, and then i add the 3.
00:41
So what does that look like? well, if i do negative 3 squared first, negative 3 times itself is a positive 9.
00:50
So you want to make sure you have a positive 9 there.
00:54
And then multiplying that positive 9 by negative 2, i get a negative 18.
01:01
And then i can take that negative 18 and add 3 to get negative 15.
01:06
And that would be the answer or the output for the first one.
01:12
For the second one, we have f of negative 2.
01:15
Sorry, input is negative 2.
01:17
And once again, this input is less than negative 1.
01:20
So we're using that top rule again.
01:23
And pretty much like what i did before, i'm going to stick in that input inside 8 parentheses to make sure that i'm squaring the negative as well.
01:34
So negative 2 squared, which is what i have to do first, becomes a positive 4, since negative times a negative is a positive...