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

Writing Polynomial Expressions When Given Roots and a Point

       306–310 Find the lowest-order polynomial that has the listed values as its zeros and whose graph passes through the given point.

      306. Zeros: –3, 1, 2

      Point:

      307. Zeros: –4, –2, 3

      Point:

      308. Zeros: –3, –2, 1, 2

      Point:

      309. Zeros: ,

Point:

      310. Zeros: 2 + i, 2 – i, –3, 2

      Point:

Graphing Polynomials

       311–316 Graph the polynomial by determining the end behavior, finding the x- and y-intercepts, and using test points between the x-intercepts.

      311.

      312.

      313.

      314.

      315.

      316.

Writing Equations from Graphs of Polynomials

       317−320 Write an equation for the given polynomial graph.

      317.

      Illustration by Thomson Digital

      318.

Illustration by Thomson Digital

      319.

      Illustration by Thomson Digital

      320.

      Illustration by Thomson Digital

Chapter 6

      Exponential and Logarithmic Functions

      Exponential and logarithmic functions go together. You wouldn’t think so at first glance, because exponential functions can look like , and logarithmic (log) functions can look like . What joins them together is that exponential functions and log functions are inverses of each other.

      Exponential and logarithmic functions can have bases that are any positive number except the number 1. The special cases are those with base 10 (common logarithms) and base e (natural logarithms), which go along with their exponential counterparts.

      The whole point of these functions is to tell you how large something is when you use a particular exponent or how big of an exponent you need in order to create a particular number. These functions are heavily used in the sciences and finance, so studying them here can pay off big time in later studies.

The Problems You’ll Work On

      In this chapter, you’ll work with exponential and logarithmic functions in the following ways:

       Evaluating exponential and log functions using the function rule

       Simplifying expressions involving exponential and log functions

       Solving exponential equations using rules involving exponents

       Solving logarithmic equations using laws of logarithms

       Graphing exponential and logarithmic functions for a better view of their powers

       Applying exponential and logarithmic functions to real-life situations

What to Watch Out For

      Don’t let common mistakes trip you up. Here are some of the challenges you’ll face when working with exponential and logarithmic functions:

       Using the rules for exponents in various operations correctly

       Applying the laws of logarithms to denominators of fractions

       Remembering the order of operations when simplifying exponential and log expressions

       Checking for extraneous roots when solving logarithmic equations

Understanding Function Notation

       321–325 Evaluate the function at the indicated points.

      321. Evaluate the function at and .

      322. Evaluate the function at and .

      323. Evaluate the function at and .

      324.