Math 116 - Chapter 3 Study Guide

No Calculators are allowed on this exam.

1. A quadratic function in standard form is given. Identify the vertex and whether the graph opens up or down.
2. A quadratic function is given. Find the y-intercept, the x-coordinate of the vertex, and whether the vertex is a maximum or minimum.
3. The vertex and a point on the parabola are given. Find the equation of the parabola.
4. List all possible rational zeros of a polynomial function. Do not find which ones are solutions, just list the possible roots.
5. Use synthetic division to show the value given is a solution to the equation and use the result to completely factor the polynomial.
6. A polynomial is evaluated using synthetic division. The value and bottom row from the synthetic division are given. Indicate whether the value is an upper bound, lower bound, or neither. Six parts.
7. A polynomial in factored form is given. Identify the leading term and the constant. Two parts.
8. Use synthetic division to evaluate a polynomial.
9. Identify the translation and determine the zeros of a transformed function. Three parts. Example, if x=-2 and x=4 are roots of a polynomial, then for g(x) = f(x+2), the translation is "left two" and so the x values (roots) would become x=-4 and x=2.
10. A portion of a polynomial function is given. Identify the leading term, the degree, the leading coefficient, the maximum number of real roots, the maximum number of turns, the right hand behavior, the left hand behavior, and the y-intercept. Two parts.
11. A polynomial function is given in both expanded and factored form. Be able to identify
    1. the number of real or complex zeros, (1 pt)
    2. the maximum number of extrema (maximums or minimums), (1 pt)
    3. the right hand behavior of the graph, (1 pt)
    4. The left hand behavior of the graph, (1 pt )
    5. the form of any possible rational zeros, (1 pt)
    6. the maximum number of positive real roots, (1 pt)
    7. the maximum number of negative real roots, (1 pt)
    8. all the real and complex zeros, (1 pts)
    9. where the graph crosses the x-axis, (1 pt)
    10. where the graph touches the x-axis, (1 pt)
    11. the y-intercept, (1 pt)
    12. the domain of the function, (1 pt)
    13. Make a sign chart for the function, (1 pt)
    14. Also be able to sketch the function. When you sketch, pay attention to the information above. (2 pts)
12. Same as #11.
13. A rational function is given in factored form. Be able to identify
    1. the domain of the function, (1 pt)
    2. simplify the function, be sure to state any restrictions that may be necessary after the simplification. (1 pt)
    3. the behavior of the graph when there is a factor in either the numerator, denominator, or both. Four parts, (4 pts)
    4. the behavior at the right and left sides [ horizontal asymptote ] (multiple choice), (1 pt)
    5. Make a sign chart for the function. (2 pts)
    6. Sketch the graph of the function. (2 pts)
14. Same as #13.
15. Write the function (in factored form) with integer coefficients which has the indicated zeros. Be aware of multiplicity and complex roots or roots with radicals. You do not need to expand the polynomial, but you do need to make sure there are no radicals, complex numbers, decimals, or fractions in the coefficients. Three Parts.
16. Write a function that has the given sign chart. Three parts.
17. Write the function whose graph could be shown. There are more than one possible function. Watch out for the exponents on factors to make the behavior turn out right. Don't forget about the number of extrema and its relation to the degree of the polynomial. Three parts.

Notes

• No calculators are allowed on this exam. The problems have been designed so that very little numerical calculations are needed and they are typically small numbers when they are. I want to see that you know what you're doing without the graphing calculator.
• Where specific problems are indicated to look at, the problem is similar to, but not exactly the same as, those problems in the book.
• Problems 11 - 14 each take one page and are like the practice problems in the classroom handouts.
• Do not spend too much time on any one problem or you will have difficulty getting through the entire test in the given time.

Points per problem

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Last updated: September 8, 2007 3:21 PM