This worksheet is an abbreviated review of the topics
covered in this class from Chapters 1 and 2. Do
this worksheet during class today. You may talk to each other, use the book,
your notes, your calculator ,
or anything else you have available to you in class right now. Turn this
worksheet in at the end of class for
a possible 5 points of extra credit to be applied to one of your first 4 tests.
Each problem is worth 1 point
of extra credit. You must get the problem completely correct in order to earn
the point. (Caution: This
worksheet does not include all of the topics covered on the test. You must still
study the other topics on
your own.)
1. Let P1 = (−2, 4) and P2 = (4, 8).
(a) Find the distance between the points P1 and P2.
(b) Find the midpoint between the points P1 and
P2.
2. Consider the equation (x − 2)2 + (y + 3)2 = 25.
(a) Find the x-intercept(s) of the equation.
(b) Graph the equation . Label the x- intercepts of the graph as well as at least
two other points on the
graph. Also, label the axis and the scale on the axis of your graph.
3. (a) Find the equation of the line which is
perpendicular to 
and contains the point (8,
3).
(b) Find the equation f(x) of the line with slope 2 such that f(1) = 10.
4. Let f(x) = x2 + 2.
(a) Find the average rate of change of f (x) from (x, f(x)) to (2, f(2)).
(b) Find the average rate of change of f(x) from (1, f(1)) to (2, f(2)).
5. The graph of the function g(x) is given be low :
Graph the function G(x) = g(−x) + 3 on the coordinate axis below.
Other topics from Chapters 1 and 2 to consider for the
final exam:
Note: This list is not com prehensive and does not refer to topics already
included in the questions on
today’s worksheet.
Finding intercepts from a graph.
Finding symmetry from a graph.
Testing for symmetry from an equation.
Graphing an equation by plotting points and finding symmetry.
Graphing a circle given the general equation of a circle (problems like §1.2
#80-88).
Finding the slope of a line.
Finding the equation of a line given the graph of a line.
Graphing lines.
Finding a line parallel to another line, through a given point.
De termining whether or not a given equation is a function.
Doing ope rations on functions : addition, subtraction , multiplication, division ,
and composition. (composition
is in Chapter 4 Section 1).
Graphing a function.
Obtaining information, such as intercepts, maxima, minima, and function values
from the graph of a
function.
Determining whether or not a function is even or odd.
Finding the intercepts of a function.
Determining where a function is increasing, decreasing or constant from its
graph.
Finding the local maxima and minima of a graph.
Finding the slope of the secant line of a function.
Remembering the functions in the library of functions. The types of functions to
remember are linear
functions, constant functions, the identity function, the square root function ,
the cube root function, the
absolute value function, the square function, the reciprocal function, and the
greatest integer function.
These are all base functions from which you can graph other functions.
Knowing how to graph functions using transformations. A problem could ask you to
graph any function
that is a transformation of one of the functions from §2.4. Transformations may
include shifts, stretches,
compressions, reflections about the x-axis, reflections about the y-axis, or a
combination of any of these.
Remember to do the reflection first, and then do the shift of the function.
Being able to construct functions from certain parameters, as in section §2.6.
Try one of each type of
problem and make sure you are able to do it.
