00:01
Here we have the graph of the function, y equals 0 .25 times 1 .2x plus 0 .8.
00:10
We have to find the domain range, any asymptopes, the x and y intercepts, whether or not this is an increasing or decreasing function, the end behavior, and the growth factor.
00:23
So let's start with the domain.
00:25
These are all the x values that are allowed by our equation.
00:32
Well, this is actually all of the x values.
00:35
There are no limitations.
00:37
So this is just going to be negative infinity to positive infinity.
00:43
The range is all of the y values.
00:48
And usually for exponential functions, there is a difference between the domain and range, especially if there are any asymptopes involved.
00:58
Well, here we can see that there is going to be an asymptope.
01:02
Where y is equal to 0 .8.
01:07
So you can have any x value you want, but it's going to stop at y equals 0 .8.
01:16
So that's going to be the bottom half of our range.
01:22
Now the top half is pretty much unlimited.
01:26
This can go to positive infinity.
01:30
And since it's positive infinity, we're going to put a bracket or a parentheses rather than a square bracket.
01:37
You don't have to write the little plus sign with the positive infinity, but i like to just because it showcases the difference between negative infinity and positive infinity.
01:47
So there is an asymptope at y equals 0 .8.
01:52
The y intercept is the point where it crosses the y axis, and i mark that on the graph, and it's 0 comma.
02:02
That little decimal there, 0 comma 1 .05.
02:07
Now, how could you read this or how can you figure this out mathematically? well, all you would do is you would place zero in place of x and then you would solve the equation...