Math 1118 - Exam 1 - topics
Covering Sections: 1.8,1.9, 2.1 - 2.5
This is not necessarily a comprehensive list but it may remind you of topics you have forgotten.
Be able to:
1. Find and interpret the difference quotient (average rate of change) for a function.
2. Determine intervals over which a function is increasing, decreasing, or constant.
3. Determine if a function is even, odd, or neither using an analytical or graphical approach.
4. Determine whether or not the graph of a function is symmetric with respect to x-axis, y-axis, or origin either using the graph or a description of the function.
5. Find the domain (from the graph or analytically) and range (from a graph or analytically when possible) of a function.
6. Graph a piecewise defined function with or without your calculator.
7. Graph any of the members of the families of functions discussed in class: linear, power (quadratic, cubic, quartic, etc) square root, cube root, absolute value, reciprocal, and greatest integer function with or without your calculator. This most likely will involve applying transformations to “simplest" family member. Be aware of the order in which the transformations are applied.
8. Use your graphing calculator to graph a function, choose a window to show a “good" global view and a “good" close-up view of the graph.
9. Sketch the graph of a transformation of an arbitrary function. The transformation may involve vertical and horizontal translations, vertical and horizontal stretches/compression's, and axis reflections.
10. Given the graph of an a function and the graph of a transformed function, find the equation of the transformed function.
11. Understand function notation, terminology.
Review
Math 1118
Sections 1.8-2.6
1. Know the distance and midpoint formulas and how to use them.
2. Know the formula for the equation of a circle, be able to find its center, radius and graph the circle.
a. Find the equation of the circle with a diameter whose endpoints are (-2, 4) and (3, 10).
b. State the center and the radius of the circle.
3. Know the term “secant line.”
4. Know the three types of symmetry and be able to determine algebraically if a relation is symmetric with respect to the x-axis, y-axis, or origin.
a. Determine algebraically if the following are symmetric with respect to the x-axis, y-axis, origin or neither.
5. Know the definitions of odd and even functions as well as how to show algebraically that a function is odd, even or neither.
6. Be able to use your graphing calculator to solve equations by the intercept technique as well as the intersection technique. Solve the following to two decimal places of accuracy.
a.
7. Be able to use your graphing calculator to solve inequalities.
a.
8. Be familiar with equations of lines: parallel lines, perpendicular lines, slopes of lines, finding the equation of a line, vertical lines, horizontal lines and applications using lines.
9. Know the difference between a function and a relation. Be able to determine from a graph if a relation is also a function.
a. Are the following graphs functions?
b. Do they have any symmetry?
i
. f(x) = 
ii.
g(x) = 
iii. h(x) = 
10. Be able to evaluate functions.
a. In the above graphs determine the following:
i. h(1) =
ii. f(.7) =
iii. what is/are the argument(s) of 1 in g(x)?
iv. what is/are the image(s) of 2 in f(x)?
11. You should have a basic library of functions that you know.
a. Power functions:
b. Root functions:
c. Absolute value functions:
f(x) = |x|
d. Greatest integer functions:
f(x) = [[x]]
e. Know the terms argument and image of a function.
f. Be able to find the domain and range of a function from a graph or from an equation.
g. Be able to evaluate and graph piecewise defined functions.
i.
Graph the following: 
Determine the domain and range of the above function.
12. Be able to apply functions to variation problems and other situations as appropriate.
a.
F varies jointly as 
and
and
inversely as r. If F = 20 when m1 = 2 and m2 = 4 and r = 5, find the constant
of variation, a formula for this relationship, and find
if
F = 20, =
3 and r = 6.
13. Average rate of change problems and the difference quotient.
a.
Find the average rate of change of f(x) =
from
a to a + h.
b. Then use this formula to find the average rate of change from 2 to 2.1.
c.
Find the average rate of change from a to a + h of
.
d. Then use this formula to find the average rate of change from 2 to 2.1.
14. Be able to determine when a graph is increasing or decreasing from a graph or by using your calculator to find maximum and minimum values.
a.
Determine the regions where the following function is increasing and
decreasing: 
15. Find the domain of the following functions:
a.
b.
16. Be able to find local maximums or minimums of a function. Use this idea to solve problems such as maximizing the volume of a box.
a. Find the local maximums and minimums of the following function.
17. Be able to use transformations to graph basic functions. Graph the following. State the domain, range and transformations applied to the parent function:
a.
b.
c.
d.
e. Given the graph of j(x) below, sketch the graph of 2j(x + 1) – 1
