Formalizing Relations and Functions

Section 4-6 Part 2

December 10, 2014

Goals

Goal• To determine whether a

relation is a function.

Rubric

Level 1 – Know the goals.

Level 2 – Fully understand the goals.

Level 3 – Use the goals to solve simple problems.

Level 4 – Use the goals to solve more advanced problems.

Level 5 – Adapts and applies the goals to different and more complex problems.

Give the domain and range of the relation. Tell whether the relation is a function. Explain.

Draw in lines to see the domain and range values

Range

Domain

Example:

Your Turn:Give the domain and range of each relation. Tell whether the relation is a function and explain.

Function Notation

• An algebraic expression that defines a function is a function rule.

• If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read “f of x,” where f names the function.

• When an equation in two variables describes a function, you can use function notation to write it.

The dependent variable is a function of the independent variable.

y is a function of x.

y = f (x)

y = f(x)

Function Notation

Input

x

The x values, can be thought of as the inputs and the y values or f (x), can be thought of as the outputs.

Output

f (x)

Function

f

Inputs & Outputs

Independentvariable

Dependentvariable

Evaluate the function for the given input values.

For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4.

Example: Evaluating Functions

Evaluate the function for the given input values.

For , find h(r) when r = 600 and when r = –12.

Example: Evaluating Functions

Evaluate the function for the given input values.

For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3.

Your Turn:

Evaluate each function for the given input values.

For g(t) = , find g(t) when t = –24 and when t = 400.

Your Turn:

Evaluate a Function

The function w(x) = 250x represents the number of words w(x) you can read in x minutes. How many words can you read in 8 minutes?

Your Turn

A car can travel 32 miles for each gallon of gasoline. The function d(x) = 32x represents the distance d(x), in miles, that the car can travel with x gallons of gasoline. The car’s fuel tank holds 17 gallons. How far can the car travel?

Identify a Reasonable Domain and Range

You have 3 quarts of paint remaining after you finished painting your 1800 square foot home. A quart of paint covers 100 ft2. The function A(q) = 100q + 1800 feet represents the area A(q), square feet, that q quarts of paint cover. What domain and range are reasonable for the function?