College Algebra Exam 3 Part 2

1. If degrees are the same on top and bottom, horizontal asymptote is y=ratio of leading coefficients. Ex: f(x)=3x/(2x-1) Answer: y=3/2 2. If degree is smaller on top, the horizontal asymptote is y=0. 3. If degree is smaller on bottom, then there is no horizontal asymptote. NOTE: Memorize the first one and check the other two situations on the calculator. Make sure to put parentheses around the top and bottom of the function when you type it in.

How do you find a horizontal asymptote?

Simplify the function. Then, set denominator equal to zero and solve. ANOTHER WAY: If you know the bad values from the domain, check those on your calculator (graph) and see if any are vertical asymptotes.

How do you find a vertical asymptote?

You must find the pretty zeros if you are doing it by hand. You can use the P/Q thing or the graph/table on the calculator. Begin factoring the polynomial using the one pretty zero at a time and synthetic division. Solve P(x)=0. Easier way: Use the factor program to factor the polynomial. It may not factor P(x) completely. Solve P(x)=0. You may need to use the square root method or the quadratic formula to solve. The solutions are the zeros.

How do you find all the actual zeros?

Divide the numerator by the denominator. The oblique asymptote is y=Quotient.

How do you find an oblique asymptote?

1. Set denominator equal to zero and solve. 2. Draw a number line and shade everything except those solutions from step 1. 3. Write the domain in interval notation with the union symbol, U, between intervals. Intervals should be smallest to biggest. NOTE: Be sure to use parentheses around the everything b/c the numbers make you divide by zero which is not possible. So, they can't be included.

How do you find the domain of a rational function?

Look at the power on the factor that the zero came from.

How do you find the multiplicities for a zero?

Let y=0 and solve for x. Basically, you get to just set the numerator equal to zero and solve for x. Write as (#, 0).

How do you find x-intercepts for rational functions?

Let x=0 and solve for y. Write as (0, #).

How do you find y-intercepts for rational functions?

1. Solve the related equation. 2. Find other critical values by setting the denominators equal to zero and solve. 3. Put the solutions from step 1 and 2 on a number line. 4. Find test values between the solutions. Plug the values into the original inequality. If the statement is true, shade that region. If the statement is false, don't shade that region. 5. Write your answer in interval notation. Smallest to biggest Note: Brackets on numbers if you have an equal to and the number does not make the denominator zero. Parentheses otherwise and on infinities.

How do you solve a rational inequality?

If the multiplicity for the zero is odd, the graph crosses. If the multiplicity for the zero is even, the graph touches.

How do you tell if a graph crosses or touches the x-axis at the zeros?