Math 100 - Study Guide for Exam 2
Section 4.1
- Evaluate expressions with positive and negative exponents without the calculator
- Use properties of exponents to simplify expressions with positive and negative exponents
Section 4.2
- Evaluate expressions with rational exponents without the calculator
- Use properties of exponents to simplify expressions with rational exponents
Section 4.3
- Sketch the graph of basic exponential functions of the form y = a^x without the
calculator. Two cases: a > 1 and 0 < a < 1
- Recognize domain, range, intercept(s), and asymptote
- Sketch the graph of more complicated exponential functions with the calculator
- Given a table, determine whether the given values suggest a function which is linear,
exponential, or neither
- Complete a table according to an exponential, or a linear pattern
- Given a table, a graph, or an equation that defines an exponential function, answer the
two types of problems
a) Find f(a)
b) Find x, when f(x) = #
Section 4.4
- Given a table of an exponential function, determine the equation of the function
- Solve power equations
- Simplify expressions containing powers
Section 5.1
- Given the table of a function, find the table for the inverse function
- Given the table of a function, answer the two types of problems
a) Find f(a),
b) Find x, when f(x) = #
1
c) Find f (a)
d) Find x, when f 1 (a) = #
- Given a function defined by an equation, find the inverse function
- Graph a function and its inverse, along with the line y = x to observe the symmetry of the
graphs
Section 5.2
- Evaluate logarithms without the calculator
- Evaluate logarithms with the change of base formula
-Graph logarithmic functions with the calculator
- Graph logarithmic functions by graphing first the inverse exponential function
- Given an exponential function, write the equation of its inverse, and use both equations to
answer the two types of problems (more of this in 5.3)
a) Find f(a),
b) Find x, when f(x) = #
c) Find f 1 (a) f 1 (a)
d) Find x, when f 1 (a) = #
- Given a logarithmic function, write the equation of its inverse, and use both equations to
answer the two types of problems (more of this in 5.3)
a) Find f(a),
b) Find x, when f(x) = #
1
1
c) Find f (a) f (a)
d) Find x, when f 1 (a) = #
- Word problems about
The Richter scale
The pH formula
The loudness of a sound
Section 5.3
- Given an exponential expression, write it in logarithmic form
- Given a logarithmic expression, write it in exponential form
- Solve logarithmic equations
- Solve exponential equations
5.4
- Solving word problems involving exponential and logarithmic equations
5.6
- Evaluating natural logarithms with the calculator
- Solving natural logarithmic equations
- Solving exponential equations with base e