[SOUND] Let's look at the domain of a function and the intercepts of it's

graph. [SOUND].

For example let's find the domain of f and any x or y intercepts of it's graph.

Let's start with the domain. What's under the square root, namely,

this x+4 has to be greater than or equal to 0, or subtracting 4 from both sides

gives us that x has to be greater than or equal to -4,

which is the domain number. So let's write that in integral notation.

Dom(f) = x has to be greater than or equal to -4 so closed bracket -4,

infinity which would be the domain. Now what about the intercepts of its

graph? Well let's let y=f(x) in other words y is equal to the square root of

(x+4) -1. Let's start by determining whether the

graph of F has any X intercepts. Well, an X intercept, if it exists, is

the X coordinate of a point where the graph of F intersects the X axis.

And on the X axis, Y is equal to 0, isn't it? Therefore if we set y equal to 0 in

our equation, we can see if there's any x intercepts.

Doing this gives us 0 as equal to the square root of x plus 4 minus 1.

And adding 1 to both sides, we get 1 is equal to the square root of X plus 4.

And then squaring both sides, we have 1 squared is equal to the square root of X

plus 4 squared. Or, 1=x+4.

And then subtracting 4 from both sides gives us x=-3.

So the graph of f does have an x-intercept.

All right, what about the y intercepts? A y intercept, if it exists, is the y

coordinate of a point where the graph of f intersects the y axis.

And on the y axis, what does x equal? It equals 0 doesn't it? So we set x=0 in our

equation here, and solve for y. So we have y equal to the square root of

0 plus 4 minus 1, or y=2-1, or y=1, which is the y

intercept of the graph of this function. Now can the graph of a function have more

than one x intercept, or more than one y intercept? There can be more than one x

intercept, but there cannot be more than one y intercept.