Sec. 1.3 – 1.4 Functions and Their Graphs

Ms. Zuniga

F239

IB Math Studies 1

I. Definitions

Relation: 2 quantities that are related to each other by some rule

Function: a relation that assigns to each element x in the set A exactly one element y in the set B

II. Mapping

Domain: all x-valuesRange: all y-valuesThe relation is a function if the x-values

don’t repeatEx.: (2,7), (4,6), (6,5), (8,6)

D R

III. Function Notation

f(x): “f of x”ex 1. If f(x) = x2 – 1, find f(-1) and f(2)Ex 2. If f(x) = x2 + 1, x<0

x – 1, x ≥0

Find f(-1)

f(0)

f(1)

IV. Find the domain of a function given its equation

Remember that in a fraction, the denominator cannot equal 0. So find what will make the denominator = 0.

Ex.1: f(x) = 1/(x2 – 4)

Ex. 2: g(x) = 1/(x+5)

Find the domain of a function given its equation

Remember that you can’t take the square root of a negative #; therefore, set whatever is INSIDE the radical sign greater than or equal to 0

Ex.1: h(x) = √(4 – x2)

Ex. 2: f(x) = 4x2 – 1

V. Vertical Line Test

Given a graph, you can determine whether it is a function or not by doing the vertical line test.

It’s NOT a function if the vertical line intersects the graph at more than one point

Vertical Line Test

Determine which of the following graphs are functions using the vertical line test

VI. Domain and Range of a Function

Determine the domain and range of the following function.