2-1 Relations & Functions

Important Terms Function: a relation in which each element in the domain is paired with exactly one element in the range Domain: set of x-values Range: set of y-values

A closer look at functions…

Ex: 1 State the domain and range and determine if the relation is a function. a){(-5, 2), (3, 0), (4, -8), (3, -9)} b){(0, 9), (5, 9), (-1, 4)} c)

Ex: 1d Domain? Range? Function?

Ex: 2 Graph y = x 2 – 1. Domain = Range = Function = One-to-one, onto, both, neither

Ex: 2a Graph: Domain = Range = Function = One-to-one, onto, both, neither

More about relations & functions…

Ex: 3 Given f(x) = x 2 + 2x, find f(3). a)f(5a) =

Ex: 3a Given h(x) = 4x – x 2, find h(n – 1).

*Challenge* Given f(x) = 4x 2 – 3x + 7,find

2-2 Linear Relations & Functions A linear function… No variables multiplied together No variables in a denominator Exponent = 1 Slope-Intercept Form: y = mx + b Standard Form: Ax + By = C – GCF of A, B, and C = 1

Ex: 1 Determine if f(x) = 3 – 4x is a linear function. If not, explain why. a)2x + xy – 3y = 0 b)6y – x = 11

Ex: 2 Paul charges $25 to test the air quality of someone’s home. The device he uses cost him $500. Write an equation that describes Paul’s net profit. How many clients does he need to break even?

Ex: 3 Write 5y = 2x + 3 in standard form.

Graphing Linear Functions Make an x-y table Slope-Intercept Form – Plot the y-int. first, then use the slope to find another point Use the x- and y-int – To find the x-int., let y = 0 – To find the y-int., let x = 0

Ex: 4 Graph 4x – 5y = 20 by finding the intercepts.

Ex: 5 Find the x- and y-int. of