Math 139A Midterm Exam
1. On your computer, select Internet Explorer, and find the
From here, enter your last name and student ID to log into the Math Placement test
system . Take test categories 6) Functions, and 7) Trigonometry. You don't need to
turn in anything for this question: I can access your scores directly.
2. Determine the formula for each of the two functions below:
(a) The function, V (t), representing the value of a home , which was purchased in
1980 (call this "t = 0") for $80; 000. The value of the home triples every 25 years.
(b) The quadratic function , f(x), containing points (-2;-18), (0; 0), and (3;-3)
3. Let .
(a) The domain of f(x): Dom(f) =
(b) The domain of g(x): Dom(g) =
(c) The domain of h(x): Dom(h) =
(d) g(f(5)) =:
4. Let f(x) = cos(x3), and g. For each, state whether the function is:
i) even, ii) odd, or iii) neither.
5. Without a calculator or computer , sketch the approximate graphs of the functions:
. Indicate which graph below corresponds to which
function. (There's one extra grid if you screw up!)
6. Compute the inverse of the following functions:
7. Simplify each of the following to determine it's value:
8. Prove any 2 of the following statements:
(a) Let f(x) be a function with domain . Then the function h(x) given
by: is even, whether f(x) is even, odd, or neither.
(b) If a function f(x) is not one-to-one, then it has no inverse function.
(c) No graph exists for the parametric curve given by:
(d) sinh(x) + cosh(x) = ex. (Hint: recall the de nitions of sinh and cosh.)
9. Use Maple for the following problem:
(a) Draw the function f(x) = sin(2x). Include gridlines, and pick a color (your choice)
for the graph . The view should be: and . Print the
(b) On your graph, draw by hand the secant line which intersects your function at
x = 0 and x = 1. Compute the slope of this secant line.
(c) What is the average rate of change of f (x) over the interval 0≤x≤1? Explicitly
explain the relationship between this average rate of change and the secant line
your just drew.