00:01
Okay, let's analyze this polynomial function.
00:05
So number one asked me to determine the end behaviors of the graph.
00:10
So we have to look at the degree of the polynomial to do this, and if i distributed that x squared, i would have x to the third plus 2x.
00:22
So this is a third degree polynomial.
00:25
That's my biggest exponent, which means 3 is odd, so that means the ends are going to be opposite.
00:35
One end's going to go up, one end's going to go down, and because this is a positive number here, it's going to look like this.
00:44
So the end behavior as f of x approaches negative infinity, sorry, as x approaches negative infinity, f of x approaches negative infinity, and as x approaches positive infinity, f of x approaches positive infinity.
01:10
So that's saying as i follow the graph to the left, it's going down, and as i follow the graph to the right, it's going up.
01:27
So it behaves like y equals x cubed, i think is what they're looking for.
01:34
Okay, part b, find the x and y intercepts of the graph of the function.
01:42
So the x intercepts are what make these x values up here equal to zero.
01:52
So what makes x squared equal zero? well, just zero.
01:57
And what makes x plus 2 equal zero? negative 2.
02:03
So the x intercepts are zero and negative 2.
02:07
The y intercept of the function is the constant of the function.
02:12
So when i distribute, i see that my constant out here is zero, so that's the y intercept of the function...