Pre-Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

Transform the points (3, 4), (–2, 6), and (5, –1) using the function description of the transformations.

      236.

      237.

      238.

      239.

      240.

Sketching Graphs Using Basic Functions and Transformations

      241–245 Find the vertex of the given function, which is a transformation of . Then sketch the graph of the new function.

      241.

      242.

      243.

      244.

245.

Sketching More Graphs Using Basic Functions and Transformations

      246–250 Find the vertical asymptote of the given function, which is a transformation of . Then sketch the graph of the new function.

      246.

      247.

      248.

      249.

      250.

Chapter 5

      Polynomials

      Polynomial functions have graphs that are smooth curves. They go from negative infinity to positive infinity in a nice, flowing fashion with no abrupt changes of direction. Pieces of polynomial functions are helpful when modeling physical situations, such as the height of a rocket shot in the air or the time a person takes to swim a lap depending on their age.

      Most of the focus on polynomial functions is in determining when the function changes from negative values to positive values or vice versa. Also of interest is when the curve hits a relatively high point or relatively low point. Some good algebra techniques go a long way toward studying these characteristics of polynomial functions.

The Problems You’ll Work On

      In this chapter, you’ll work with polynomial functions in the following ways:

       Solving quadratic equations by factoring or using the quadratic formula

       Rewriting quadratic equations by completing the square

       Factoring polynomials by using grouping

       Looking for rational roots of polynomials by using the rational root theorem

       Counting real roots with Descartes’s rule of signs

       Using synthetic division to quickly compute factors

       Writing equations of polynomials given roots and other information

       Graphing polynomials by using end-behavior and the factored form

What to Watch Out For

      Don’t let common mistakes trip you up; keep in mind that when working with polynomial functions, your challenges will include

       Watching the order of operations when using the quadratic formula

       Adding to both sides when completing the square

       Remembering to insert zeros for missing terms when using synthetic division

       Recognizing the effect of imaginary roots on the graph of a polynomial

Using Factoring to Solve Quadratic Equations

       251–260 Find the solution set for the equation by factoring.

      251.

      252.

      253.

      254.

      255.

      256.

      257.

      258.

      259.

260.

Solving Quadratic Equations by Using the Quadratic Formula

       261–265 Use the quadratic formula to solve the equation.

      261.

      262.

      263.

      264.

      265.

Using