Math 116: Study Guide - Chapter 3
- Sketch the graph of the function. Identify the vertex, intercepts, and zeros of the function.
Look at problems 3.1.13 - 3.1.21.
- Find the equation of the parabola with the given vertex and passing through the given point.
Look at problems 3.1.31 - 3.1.35.
- Use synthetic division to show the value given is a solution to the equation and use the result
to completely factor the polynomial. Look at problems 3.3.41 - 3.3.47.
- 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. (4 parts).
- A polynomial function is given in both expanded and factored form. Be able to identify the
number of real or complex zeros, the maximum number of extrema (maximums or minimums),
the right and left hand behavior, the form of any possible rational zeros, the maximum number
of positive and negative real roots, all the zeros, where the graph crosses and touches the x-axis, the y-intercept, and the domain of the function. Also be able to sketch the function.
When you sketch, pay attention to the information above.
- A rational function is given in factored form. Be able to identify the domain of the function,
the behavior of the graph when there is a common factor between numerator and denominator
(multiple choice), for what values in the domain of the function will the graph cross or touch
the x-axis, the behavior at the right and left sides [ horizontal asymptote ] (multiple choice),
where the graph is asymptotic in the same and different directions to a vertical line. Sketch the
graph of the function.
- 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.
- Determine, if possible, the zeros of a transformed function. Look at problems 3.3.87 - 3.3.92
(could be even). Three parts.
- True or False. Know ...
- That complex solutions involving i come in pairs.
- Polynomials are continuous, but rational functions aren't.
- What continuous means.
- When an oblique asymptote occurs.
- The role of the being able to sketch functions by hand when there are graphing
calculators which will do it for you.
- What the Intermediate Value Theorem does and does not guarantee.
- Where specific problems are indicated to look at, the problem is straight from the text.