Question

Will fan! Please help

Answer 1

Identify the discontinuities, graph, and find the zeros of each rational function

Answer 2

I really just need help starting it off

Answer 3

@mathstudent55

Answer 4

Look at the function. It is a fraction with a polynomial in the numerator and a polynomal in the denominator.

Answer 5

Now think of the numerator, is there any value of x that you can think of that could cause a problem in the numerator? Can all reall numbers be used for x in the numerator?

Answer 6

oh okay
What confuses me is that I am used to being able to factor it but I don't know how to do that here

Answer 7

Now look at the denominator. A denominator cannopt be zero. Is there a value of x that would cause the denominator to be zero? The only thing that can cause a discontinuity in this funcrtion is a zero in the denominator. Set the denominator equal to zero, and solve for x.

Answer 8

-10

Answer 9

The numerator can be factored.
It is the famous difference of two squares which factors as follows:

\(a^2 - b^2 = (a + b)(a - b) \)

Here you have

\( x^2 - 100 = x^2 - 10^2 \)

As you can see, you do have the difference of two squares:

\(x^2 - 10^2\)

Answer 10

x = -10 is the dicontinuity. You are correct.
Now to graph it, factor the numerator, divide it by the denominator and graph it as a line with an open cirlce at the point where x = -10.

Answer 11

Once again, factor the numerator. Use the difference of squares pattern I gave you above. What does the numerator factor into?

Answer 12

Then how would I find the zeros? And the point? Because in the hw notes it says basically you find f(x), then point of discontinuities,then the point, and then the zeros

Answer 13

If that is the numerator then I got it! ( how to do the rest)

Answer 14

You have the dicontinuity already.
To graph, factor the numerator and divide it by the denominator. You will get a linear function with a discontinuity at x = -10.
Then set the simplified function (after dividing) equal to zero, and solve for x to find the xero.

Answer 15

Oh okay thanks soo much that numerator had me confused!

Answer 16

Great. You factored the numerator correctly.
Keep the function always together. This is what your work should look like:

\( f(x) = \dfrac{x^2-100}{x + 10} \)

\( f(x) = \dfrac{(x + 10)(x - 10)}{x + 10} \)

\(f(x) = x - 10, ~x \ne 0 \)

Answer 17

Yup that is what I have thanks again :)!

Answer 18

After the division, when the function looks simply like this:

\(f(x) = x - 10, ~x \ne 0 \)

You can see that the function is a linear function.
Graphing now is simple. Finding the zero means simply set x - 10 = 0 and solve for x.
Remember that when you grpah, at the point where x = -10, you need to place an open circle to show the discontinuity at that point.

Answer 19

You're welcome.