MA 16500 Study Guide - Fall 2018, Comprehensive Midterm Notes - Trigonometric Functions, Zwiefalter Aach, X Window System
12 Oct 2018
School
Department
Course
Professor
MA 16500
MIDTERM EXAM
STUDY GUIDE
Fall 2018
1. What is a function?
Answer: A rule that assigns to a member x a unique value f(x)
Example of function: (x)f=x2
x
(x)f
1
1
2
4
3
9
Example of function: (x)os(x)f=c
is a function if it meets each vertical line line test(x)f
Example (not a function): x=y2
Violates vertical line test because x (the input) gives 2 contradictory values (the output).
2. What is a slope?
Answer: Describes the direction and the steepness of a line
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Example: (x)x f= 2 − 1
In this case, the slope is 2, as when the x value increases per 1 unit, the y value goes up 2 units.
What about quadratic functions? Quadratic function do not have a consistent slope, like linear
functions do. They have a certain slope at a certain point, and we can find them out as follows:
Example: (x)f=x2+ 1
We use the formula to find the slope of the function at certain pointslim
h → 0 h
f(x+h)−f(x)
xxxlim
h → 0 h
f(x+h)−f(x)= lim
h → 0 h
(x+h) +1−x−1
22=h
x−x+2xh+h+1−1
2 2 2= 2 + h= 2 + 0 = 2
Thus the slope of at certain points is 2x. For example, if we have an x value of 8,f(x) = x2+ 1
the slope of the function is 16.
3. Domain
What is the domain? It’s which values you can plug into (x)f
Examples:
(x)f=√x+ 2
Domain: − , )[ 2 ∞
(x)f=1
x−x
2=1
x(x−1)
Domain: − , ) 0, ) 1, )( ∞ 0 ⋃( 1 ⋃( ∞
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