MA 16500 Lecture Notes - Lecture 1: Quadratic Function
6 Jun 2018
School
Department
Course
Professor
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
Document Summary
Answer: a rule that assigns to a member x a unique value f(x) = c os(x) is a function if it meets each vertical line line test (x) f. Answer: describes the direction and the steepness of a line f. In this case, the slope is 2, as when the x value increases per 1 unit, the y value goes up 2 units. 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: We use the formula to find the slope of the function at certain points f(x+h) f(x) f. = x2 + 1 lim h 0 h. 2 h (x+h) +1 x 1 f(x+h) f(x) = lim lim h 0 h 0 f(x) = x2 + 1. Thus the slope of the slope of the function is 16. h.
