Unit 1

• Find vertical asymptotes by factoring the numerator.
• If the denominator's degree dominates, the horizontal asymptote is y=0.
• If the numerator's degree dominates, there is no horizontal asymptote.
• If the numerator's degree = denominator's degree, the horizontal asymptote is the ratio of the leading coefficients.
• X-intercepts are found by factoring the numerator.
• For odd functions, f(-x) = -f(x).
• For even functions, f(-x) = f(x).
• A function is even if it can reflect over the y-axis.
• A function is odd if the function is symmetric 180 degrees about the origin.
• Increasing ROC = the 1st difference is going up.
• Decreasing ROC = the 1st difference is going down.
• Concave up makes a valley shape.
• Concave down makes a hill shape.
• Increasing ROC = concave up.
• Decreasing ROC = concave down.
• Function is increasing = line goes up as it goes right.
• Function is decreasing = line goes down as it goes right.
• Function is positive = stays above y-axis.
• Function is negative = stays below x-axis.
• AROC is the slope between the first and last points.
• Slope is rise/run.

  
• Positive ROC = function is increasing.
• Negative ROC = function is decreasing.
• 1st difference = 1st degree, 2nd difference = 2nd degree, etc.
• The degree of a function is how many roots it has.
• Turns on graph = points of inflection.
• The amount of turns on a graph + 1 = the least possible degree.
• Right end behavior is to positive infinity if the leading coefficient is positive.
• Right end behavior is to negative infinity if the leading coefficient is negative.
• Left end behavior is the same as right end behavior if the function degree is even.
• Left end behavior is the opposite of right end behavior if the function degree is odd.
• If a root has an even multiplicity, it bounces.
• If a root has an odd multiplicity, it passes.
• If a vertical asymptote has an even multiplicity, the function will approach it the same way on each side.
• If a vertical asymptote has an odd multiplicity, the function will approach it differently on either side.
• Zeros from the denominator are undefined.
• Test for intervals by using the number line method.