Math 139A - Midterm Exam 1

1. Identify the specified function with both i) a formula , (such as f(x) = ...), and ii) a
graph drawn on the grid provided.

(a) The linear function which contains points (-2, 4), and (4, 1):

(b) The quadratic function containing points (-1, 0), (0,-3), and (2, 3)

2. For each function listed below, de termine if it 's: i) even, ii) odd, or iii) neither:

(c) Consider the function f(x) below, defined for the moment only on the interval
0 ≤x ≤5. On the left, sketch an extension of the function needed to make the
entire function an EVEN function. On the right, sketch an extension of the function
needed to make the entire function an ODD function. Note: These are called the
\even and odd extensions of f(x)".

3. Compute the average change of the function over the given interval for:

(a) The distance travelled, d(t), (in miles) between 1:00 pm and 4:00 pm, from the
table:

(b) f(x) = x² + x over the interval 3≤x ≤8.

(c) r(t) given in the graph below , for -3 ≤t ≤2.

4. LetComplete any 5 of the
6 parts below:

(a) The domain of s(x), Dom(s) =:
(b) The domain of q(x), Dom(q) =:
(c) r(p(s(x))) =:
(d) s^-1(x) =:
(e) The domain of r(q(x)), Dom(r(q(x))) =:
(f) The domain of p(x) r(x) q(x), Dom(p(x)r(x)q(x)) =:

5. Without a calculator or computer , sketch the approximate graphs of the functions:
Indicate which graph be low corresponds to which func-
tion. (There's one extra grid if you screw up!)

6. Let f(x) be given in the first graph below. Determine the graph
using the blank grids for intermediate steps .

7. Let f(x) = cos(2x) + 1:7 and g(x) = sin(x) + x².

(a) Use MAPLE to draw, in the same gure, f(x), g(x). Use gridlines, and include
a title, make the plots green and plum respectively, and show which function
corresponds to which color using a legend. The view should be: -5 ≤x ≤5
and -5≤ y ≤5

(b) From your graph, find the TWO approximate solutions, x =..., to the equa-
tion: cos(2x) + 1.7 = sin(x) + x². Both answers should be correct to within
±1/4 . Print your graph out, circle these two points on your graph, and include
it when you turn in your test.

(c) For the solution on the right , zoom into the point by resizing your window
until you can determine the value of the solution correctly to within ±0.001