MATH 180 – STUDY GUIDES – Chapter 5 -6TH EDTION

Section 5.1 – Composite Functions

  1. Evaluate composite functions
  1. Find the composite function and its domain (rational functions included)
  1. Solve word problems involving composition of functions
  1. Given a function H, find functions F and G so that H = F o G

Section 5.2 – Inverse Functions

  1. Determine whether the function is one to one (From an equation)
  1. Find the inverse of one to one functions

From a graph

From an equation (rational functions included)

  1. Given the graph of a one to one function, sketch the graph of its inverse
  1. Given a pair of inverse functions, show that their composition is x
  1. State the domain and range of a function and its inverse
  1. Solve word problems involving inverse functions

Section 5.3 – Exponential Functions(study boxed in problems 91-100 page 285)

  1. Evaluate exponential expressions with the calculator
  1. Recognize tables of exponential functions and write the corresponding function
  1. Sketch the basic exponential functions and give domain, range, intercepts, and asymptotes (, for , and for ). (base e also included)
  1. Sketch the graph of exponential functions using transformations and give domain, range, intercepts, and asymptote (basic problems)
  1. Solve exponential equations in which both sides can be written as a power of the same number
  1. Solve word problems involving exponential functions(Evaluation type)
  1. Find inverses of exponential functions and give domain and range of each

Section 5.4 – Logarithmic Functions(study boxed in problems 111-116 page 299)

  1. Change an exponential expression to an equivalent logarithmic expression
  1. Change a logarithmic expression to an equivalent exponential expression
  1. Evaluate logarithmic expressions with and without the calculator
  1. Find the domain of a logarithmic function
  1. Sketch the basic logarithmic functions and give domain, range, intercepts, and asymptote (,for , and for )
  1. Sketch the graph of logarithmic functions using transformations and give domain, range, intercepts, and asymptote
  1. Solve exponential and logarithmic equations
  1. Solve word problems involving logarithmic and exponential functions

a) Evaluation type and

b) Equation type

  1. Find inverses of logarithmic functions and give domain and range of each

Section 5.5 – Properties of Logarithms (study boxed in problems 85-86 page 309)

  1. Evaluate logarithmic expressions without the calculator
  1. Write a logarithmic expression as a sum or difference of logarithms (expand using properties of logarithms)
  1. Write an expression as a single logarithm
  1. Evaluate logarithms by using the change of base formula
  1. Graph logarithmic functions with the calculator using the change of base formula
  1. Solve logarithmic equations and express y as a function of x

Section 5.6 – Logarithmic and Exponential Equations(study boxed in problems 87-96 page 316)

  1. Solve exponential equations: Steps: Isolate the exponential expression

Solve by using logs

  1. Solve logarithmic equations: Steps:Take to format Log  = Log O, or Log  = # (any base)

Solve by exponentiation (with the same base)

  1. Solve exponential and logarithmic equations with the calculator

Section 5.8 – Applications

In all the following types word problems you should be able to

a) Construct the equation satisfying the given conditions

(That is, find the constants of the equation)

b) Answer the two kinds of problems:

a) Given x, find y (Evaluation type)

b) Given y, find x (Equation type)

c) Find intercepts and interpret within context

d) Find asymptotes and interpret within context

  1. Word problems about uninhibited growth

Also, find the growth rate, and the doubling time

  1. Word problems about uninhibited decay

Also, find decay rate, and the half-life

  1. Word problems using the Newton’s law of cooling

Also, find asymptote and interpret within context

  1. Word problems using the logistic model (optional)

Also, find carrying capacity, inflection point, asymptotes

Recognize the increasing and the decreasing case

Section 5.9 – More Applications

(OYO – similar to linear regression procedure: Sketch scatter-diagram with calculator, identify the function and use the corresponding regression in the calculator)

  1. Using regression analysis in the calculator to find the

a) Exponential model

b) Logarithmic model

c) Logistic model

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