Math 121-Additional Practice Problems
The final exam for Math 121 will be cumulative. It will be a mixture of multiple choice questions and
problems to complete by showing your work. No note cards, cell phone/calculators will be allowed. To
prepare, you should redo all past exams and quizzes, work through all of the previous reviews, and look over
your homework for the term. Any material covered on those could be on the final exam. These are some
additional problems if you would like more practice. Try to work this entire problem set as you would a
test. No notes, a quiet space, and give yourself two hours. Math finals can be particularly stressful so give
yourself some practice before the big day. Study hard and good luck!
1. For the circle in x2+ (y−1)2= 16 standard form
(a) State the center and radius.
(b) Determine the intercepts.
Note: Make sure you can write a circle given in general form in standard form by completing the
square!
2. Determine the distance between the points (3,−5) and (2,7). What is the midpoint?
3. For the function f(x) = 1 −2x2, compute the difference quotient f(x+h)−f(x)
hand simplify.
4. Find the average rate of change of f(x) = x3+ 2 from x= 1 to x= 3.
5. Be able to graph all of the basic graphs we discussed during the term. You should know all of the
graphs from section 3.4 (Library of Functions), the graphs of exponential and logarithmic functions,
and be able to apply transformation using these basic graphs. You should also be able to determine
the domains of any function we have discussed this term.
6. Given the rational function f(x) = 2x2−3x+4
x3−2x2−3x, determine
(a) The domain of f.
(b) Any asymptotes of f.
7. For the polynomial function f(x)=(x+ 2)(x−1)2
(a) Find the zeros and their multiplicities.
(b) State the behavior of the graph at each zero (does it cross or touch the x-axis).
(c) Determine the end behavior of the graph.
(d) Sketch the graph, labeling the zeros.
8. Given the quadratic function f(x) = x2−4x+ 2
(a) Determine the domain and range.
(b) Determine the vertex and axis of symmetry.
(c) Find all the intercepts
(d) Graph the function and label the vertex and intercepts.
9. Given f(x)=2x2+ 3 and g(x) = √x−1.
(a) Compute the compositions (f◦g)(x) and (g◦f)(x) and simplify.
(b) What is the domain of f◦g? Write your answer using interval notation or set-builder notation.
(c) What is (g◦f)(1)?
