Math 112 Calculus Learning Goals
Section 1.1 and 1.2:
Ways to represent a function/ Mathematical models
1. Function review.
Given a function, find its domain, range, value at a given point, intervals where it
increases/decreases, both graphically and algebraically.
Online: o2, o3, o4, o6)
2. Convert one representation of a function to another, including for piecewise functions, linear functions, polynomials,
power functions, trig, exponential, and log functions.
- verbal to/from graphical
(Written: 1.1: 12, 21;
1.2: 4; Online:
-algebraic to/from graphical
(Written: 1.1: 46, 55; 1.2: 8; Online o5, o10)
-verbal to/from algebraic
(Written: 1.2: 16; Online o8, o9, o11, o12)
3. Show a function is even or odd or neither.
Identify even and odd functions algebraically and graphically.
72; Online: o7).
Section 1.3: New functions from old
Apply and recognize transformations of functions:
Given a graph which is a transformation of a known function, find an
Given a formula, find the graph.
(Written 1.3: 1, 7, 13, 21; Online o1, o2, o3, o4)
Given functions f and g, find: f+g, f-g, fg, f/g, and their domains.
(Written: 1.3: 30; Online o5)
Understand and apply compositions of functions: Given functions f, g, and h, find g o f, f o g, f o g o h, etc.
Given f o g,
find functions f and g.
Similarly for f o g o h.
(Written 1.3: 33, 47, 55; Online o6, o7, o8)
Section Appendix D:
1. Given angles in degrees and radians, draw the angle, convert from radians to degrees and vice versa, and, for the
angles 0, pi/6, pi/4, pi/3, pi/2 and angles obtained from these by adding a multiple of pi/2, find sin, cos, tan, sec, csc, cot of
(Written AppdxD: 24, 27, o1)
Given a right triangle with side measurements, find sin, cos, tan, sec, csc, cot of any of the angles of the triangle in
terms of the side lengths. Use right triangles with given measurements to find other measurements.
(Written: AppdxD: 37;
Online o2, o3, o4)
3. Graph trig functions.
(Written AppdxD: 79; Online o5, o6)
Use trig identities to simplify expressions, and to solve equations and inequalities involving trig functions.
AppdxD: 46, 53, 73; Online o7, o8)
Most important identities:
(x) + cos
(x) = 1, (b) sin(-x) = -sin(x), cos(-x) = cos(x),
(c) sin(x+y) = sin(x)cos(y) + cos(x)sin(y),
cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
Using the above identities, derive other identities:
(x) = csc
(e) sin(x-y), cos(x-y),
(f) sin(2x), cos(2x)
1. Graph exponential functions a
for a<1, a>1, as well as transformations of exponential functions from section 1.3. Find
(Written 1.5: 11, 12, 19; Online o1, o2)
2. Given two points on the graph of an exponential function, find the equation of the exponential function
. (Written 1.5:21,