00:06
All right.
00:09
So we have four curves that we have to sketch, and they're based on the graph of y equals x to the fifth power.
00:19
The graph of y equals x to the fifth power looks like the graph of the cubic function.
00:27
So in other words, it comes like this.
00:29
It flattens out a little bit here in the middle and goes back up.
00:35
So that's the parent function that we're going to be basing all of our graphs on.
00:40
And we're going to graph using the rules of transformations.
00:46
So if p of x is equal to x plus three to the fifth power, then this is going to be the graph of x to the fifth power.
00:58
Now this plus three is being added to the x.
01:00
It's inside the function.
01:03
This right here is a shift to the left of three units.
01:13
So when we sketch this, the coordinate that would ordinarily be at the origin, instead is going to be over here at negative 3 -0, and we're just going to simply have a curve that looks just like the original does that's passing through that coordinate.
01:35
So we have an x intercept at negative 3 -0.
01:41
That will be our x intercept, and our y intercept is going to be right here where x is equal to zero.
01:48
Well, if we plug zero in for x, we're going to get 3 to the 5th power, and this right here is going to be the coordinate 0, 243.
02:00
So that's our y intercept, and our x intercept is at negative 3 .0.
02:05
The second function we want to look at then, q of x, is going to be 2 times x plus 3 to the 5th power, minus 64.
02:23
So there's three transformations going on with this one.
02:27
We have a shift to the left of three units, just like the first one.
02:32
So we're going to the left three.
02:36
This right here, outside the function, it's not being raised to the fifth power.
02:39
So that's a change to the y.
02:41
So this is a shift down 64 units.
02:47
And here, we're multiplying the function by two.
02:51
That's going to be a vertical stretch by a factor of two.
02:59
In other words, we're doubling all of the y values.
03:02
So what is this going to end up looking like? well, this coordinate, once again, that's normally at the origin, is getting shifted to the left three units, but it's also getting shifted down 64 units.
03:26
So we're going to have this curve that's coming up and doing something like this.
03:36
So what do we have going on for intercepts? well, y intercept is going to be, actually our y intercept should be above the x axis, shouldn't it? it's going to be a positive value.
03:57
It's going to be getting large quickly, because if we let x equal zero, then q of zero is going to be two times zero plus three to the fifth power minus 64.
04:21
That's going to be two times 243 minus 64.
04:27
That's going to give us a y intercept of 422...