# STUDY GUIDE FOR MATH 2147 TEST ONE

The textbook sections of Test One are R.8, 3.1, 3.5, 6.2, 6.3, and 6.4. A section by section breakdown of the test objectives with corresponding hw problems to practice are given below:

SECTION R.8- NTH ROOTS , RATIONAL EXPONENTS

Simplifying expressions containing rational exponents are radicals. HW #67-87 odds

SECTION 3.1-FUNCTIONS

•Using function notation HW #39-46 ALL

•Finding the domain of a function HW #51-60 ALL

•Computing the difference quotient of a given function HW #74,75,77,79, 80 (for
#79, use 3

SECTION 3.5- GRAPHING TECHNIQUES , TRANSFORMATIONS

•Sketch the graph of a function using transformations (shifts, reflections,
stretching, and shrinking)

HW #35-61 odds, 65-68, 75-83 odds

SECTION 6.2-ONE-TO-ONE FUNCTIONS, INVERSE FUNCTIONS

•Given the graph of a one-to-one function f, sketch the graph of the inverse
function f^{-1}. HW #41-46 ALL

•Find the inverse f^{-1} of a given one-to-one function f. State the domain and
range of both f and f^{-1}. Also, if directed to do so, sketch the graphs of f,
f^{-1}, and y=x on the same set of coordinate axes. HW #49-69 odds

•Apply inverse functions to real -life situations. HW #89, 91-94 ALL. Also, try
#95. It is an interesting problem.

SECTION 6.3 EXPONENTIAL FUNCTIONS

•Use transformations to sketch the graph of a function with an exponential term .
Find the domain, range, and horizontal asymptote of each function. HW #37-55
odds

• Solve exponential equations. HW #57-75 odds

• Solve general problems involving the concept of exponential function. HW #77-90
odds

•Graph piecewise defined functions involving exponential terms HW #90-94 ALL

SECTION 6.4- LOGARITHMIC FUNCTIONS

•Write an equation in exponential form into logarithmic form and vica versa. HW
#9-35 odds

•Find the exact value of a logarithmic expression without using a calculator .

•Find the domain of functions with logarithmic terms , HW #37-48 ALL

•Sketch the graph of a one-to-one function f with logarithmic terms and its
inverse f^{-1}. Find the domain , range, and vertical asymptotes.

•Solve logarithmic equations. HW #87-111 odds

•Use logarithms to solve real -life problems. HW #117-133 odds

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