Functions and Graphs in Math 1310: Definitions, Examples, and Vertical Line Test - Prof. B, Exams of Algebra

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Math 1310

Chapter 3, Section 3.2 –

Functions and Graphs

B. Constante

Definition:Let

f^

be a function with domain A. The

graph

of the

function f is given by {(x, y)| x is an element in A}. The graph is the set of all points (x, y) in the coordinate

plane whose x-coordinates are elements of the domain Aand whose corresponding y-coordinates are given byy=f(x).

Example 1: Determine whether or not each of the following

graphs represents a function. a.

b.

Example 2: The graph of y = f(x) is shown below.a. Find the domain of the function.b. Find the range of the function.c. Find the following function values:f(0) f(-3)

b. f(x) =

2

x

c. f(x) =

1^ x

e. f(x) =

3 x

Example 4: Find the domain of the function and graph the

function.

2

) (^

=^

x

x f

Example 6: Determine whether the following equation

defines y as a function of x.

1. Solve for y. 2. For each value of x that we can substitute into the

equation above, do we get back exactly one value for y?

3

y

x

Example 7: Determine whether the following equation

defines y as a function of x.

1. Solve for y.2. For each value of x that we can substitute into the

equation above, do we get back exactly one value for y?

2

x

y