What is a function?

The Vertical Line Test

can determine if a graph is a function. If the vertical line passes through two or more points on a graph of a relation, then the relation is NOT a function.

What is the f(x) = -4x^2 + 5, when x = -3?

f(-3) = -4(-3)^2 + 5 f(-3) = -4(-3)(-3) + 5 f(-3) = -36 + 5 f(-3) = -31

Evaluate f(x) = -4x^2 + 5, when x = 1?

f(1) = -4(1)^2 + 5 f(1) = -4(1)(1) + 5 f(1) = -4 + 5 f(1) = 1

A relation is not a function

when an input has two different outputs. In this case, the input value -1 has two out put values.

The domain or input values of a function is the

set of x-coordinates in a relation.

The range or output of a function is the

set of y-coordinates in a relation.

A function is

a relation in which each element of the domain is paired with exactly one element of the range

A relation is

a set of ordered pairs

The x-intercept of a function

is the point where the graph crosses the x-axis.

The y-intercept of a function

is the y-coordinate of where a graph crosses the y-axis. To find the y intercept of any function, set x = 0, then simplify the algebraic expression.

Function notation is a

is when we use f(x) or g(x) to represent a specific function instead of using y.

The value of the y coordinate at all x-intercepts

is zero.