Honors PreCalculus - Chapter 2 Review

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When you're asked to graph a polynomial of a degree higher than 3...
Use your calculator and check the positive and negative values. (You can solve for the x-intercepts end behavior).
When you're asked to find all the factors and solutions to a polynomial...
Use your calculator, find all whole-number x-intercepts, Foil them together (if needed), divide them by the original equation, and then factor the dividend. Remember to SIMPLIFY ALL RADICALS
When asked to find Vertical Asymptotes...
Set the DENOMINATOR equal to zero.
When asked to find Horizontal Asymptotes...
Use the degrees...
-If the numerator and denominator degrees are the same, then divide the two leading coefficients.
-If the numerator has a smaller degree, then this number is 1.
-If the numerator has a larger degree, then there is none.
When asked to find Holes...
Find any two factors in the numerator and denominator that can be "crossed out".
When asked to find a Slant Asymptote...
Look to see if there is an unfactored polynomial in the numerator, or a numerator x is squared. If there is, then there is one [of the specified terms]. (If not, then there are none). The y-intercept of this can be found in the denominator.
When asked to solve a Rational Function...
Multiply each term by the missing term, and match up all of the denominators. Then, "cross out" all of the denominators and solve the equation left over from the remaining numerators.
How to find the End Behavior...
Use the leading coefficient. If the function is factored, then multiply the largest degree x's within each factor together. Remember to multiply the x's, but to add the degrees (rather than multiply them).
Use the leading co-efficient to determine this [specified term] based on it's positive/negativity, and whether its degree is even or odd.
When asked to solve an Inequality...
-If it is not a fraction, then it is a "Polynomial". Simplify it, find it's end behavior and x-intercepts. Then, graph it (or use a x/y chart) and find negative and positive areas.
-If it is on a fraction, then it is "Rational". Simplify it, and then find the x-intercepts and the x-asymptotes. Then make an x/y chart and plot x values on the ends and in-between the numbers you found. Figure out the pattern of negatives and positives, and then solve the [specified term] equation.