00:01
We are given this function, f of x, a piecewise function which is as follows, 2x plus 3 if x is less than 4, and x squared plus 4, if x squared plus 4, if x is greater than or equal to 4.
00:27
We're asked to find a, f at negative 2, b, f at 7, and we're asked to find the y intercept for part c.
00:48
All right, so let's dig in.
00:51
This is going to be a, where we're to find what f of x is at negative 2.
01:02
We see that negative 2 is less than 4.
01:09
It is not greater than or equal to 4.
01:14
So we're going to have to use the first piece of the function.
01:20
So that means that f of x is equal to 2 times negative 2 plus 3.
01:31
And this should be negative 4 plus 3, which will be negative 1.
01:42
We're to find f of x at 7.
01:48
Here, 7 is not less than or equal to 4, but it is greater than 4.
02:03
And so we're going to use the second piece of the function, which is of x at 7, is x square which is seven square plus four which would be 49 plus 4 which is just going to give us 50 now part c we had to find the y intercept note that the y intercept curves where x is equal to zero and so what we're looking for is f of x at 0.
02:58
0 is less than 4, but 0 is not greater than or equal to 4.
03:07
So we get to use this piece of the function...