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Material Type: Notes; Class: College Algebra; Subject: Mathematics; University: Pellissippi State Technical Community College; Term: Unknown 1989;
Typology: Study notes
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Name: Date: Instructor:
Topics: Relations, Functions, Domain, Range, Evaluation, Increasing, Decreasing and Constant Functions
I. Relations and Functions (pp.197 – 199)
A ______________is a _____ of ordered pairs. A _____________ is a relation in which, for each value of the _________ component of the ordered pairs, there is ___________ _________ value of the second component. *There are no repeated x values.
Ex. Given a set of ordered pairs, decide whether each relation defines a function. a. { (2, 4), (0, 2), (2, 5) }
b. { (-3, 1), (4, 1), (-2, 7) }
Ex. Given a graph, decide whether the relation defines a function.
Sketch the graph in the video. Name the two points that are highlighted as the reason that the graph does not represent a function: _____________ and _______________
The result above indicates that to be a graph of a function, the graph must pass the ________________ __________ _________, which states that if a ______________ line intersects a graph in at most ________ point, then the graph is that of a function.
Given an equation, decide whether the relation is a function or not. *Choose values that demonstrate there is more than one value that results from the number you chose. Ex. x = y^6
Ex. y = 2 x – 6
II. Domain and Range of a Function (pp. 199 – 204)
The values that x can have is called the _______________. Sometimes this is called the “input value”. The values that y can have is called the _______________. Sometimes this is called the “output value.”
Ex. State the domain and the range for the functions below. Write the answer using interval notation. a. y = 2 x – 6
Domain:
Range:
b. x = y^6
Domain:
Range:
III. Notation for Functions (pp. 204 – 207)
Functions are written in a more formal style using f(x) and is read “ f of x ”. This is not multiplication, but is a more concise way of writing an equation with the particular characteristic of no repeated x coordinates. When you evaluate a function , you’re being asked to substitute the value from the domain (the x coordinate) and find the value of the range that results (the y coordinate). *Pay attention to the instructions… that’s where the functions are defined, to be used throughout the parts of the problem.
Ex. Let f (x)= – 3 x + 4 and g (x) = – x^2 + 4 x + 1. Find:
a. g (-2)
b. f ( 2 m – 3)
Ex. An equation that defines y as a function of x is given. Solve for y in terms of x and replace y with the function notation. Find f (3). *The “replacement of y with the function notation” will dress the equation up a bit… makes it more formal. 4 x – 3 y = 8
When the x value is 3, then the y value is _______.