Math Chapter 6 "Relations and functions"

Which of the following ordered pairs is not an element of the function f(x)=x−5?

(0,5)

Generally, a relation is just a collection of

A relation is a collection of ordered pairs (x,y) wherein x is related to y.

merry-go-round can complete 1 revolution in 1 minute. Write a function that represents how many revolutions the merry-go-round can complete in x number of minutes.

If the merry-go-round can complete a revolution in 1 minute, then it can complete 2 revolutions in 2 minutes, 3 revolutions in 3 minutes, and so forth. Therefore, the number of revolutions it can complete in x number of minutes is given by the function f(x)=x.

A cheetah can cover a distance of 120 miles in 1 hour. Which of the following functions determine how many miles a cheetah can cover in x number of hours.

Multiply x (number of hours) by the rate at which the cheetah can cover distance in an hour. f(x) = 120x

A ball was dropped from the top of a building. The height of the ball x seconds after it was dropped is given by the function f(x)=−9.8x2+200. Determine the range of the function.

Since the height of the ball cannot be a negative number, the range of the function is 0≤y≤200.

mapping diagram

The figure formed from the circles and arrow

Determine the dependent variable in the function defined by the equation y=x+2

The value of y depends on the choice of x.

How do we formally define a function as a set of ordered pair (x,y)?

no two distinct pairs have the same first number

In a function, it is the set of all possible values of the dependent variable.

range of a function

The most common way to write a function

using the f(x) notation (read as "f of x").

Which of the following defines a function wherein the y value is obtained by adding 3 to each value of x?

The function f(x)=x+3 defines an equation wherein the corresponding value of y is obtained by adding 3 to a specified value of x.

Determine the independent variable in the function defined by the equation y=x+2.

The variable x is the independent variable because its value does not depend on anything.

In a function, an x value must only be paired with a unique value of y. However, a distinct y value can be paired with multiple values of x.

True

How can we descive the relation of one set to another?

We can describe the relation of one set to another as a diagram that illustrates which element(s) of the first set correspond(s) to which element(s) of the second set.

Determine which of the following ordered pairs is not an element of the relation defined by y=x−2

When x=0, the value of y should be −2.

Equation

a rule by which a unique value of is assigned to a value of x.

Function

a set of ordered pairs wherein an x value must only be paired with a unique value of y.

independent variable

a variable (often denoted by x ) whose variation does not depend on that of another.

dependent variable

a variable (often denoted by y ) whose value depends on that of another.

What do we call the set of all admissible values of x for any function f(x)?

domain of a function

The parking fee in mall parking lots is described by the function f(x)=45x where x is the number of hours. Determine the range of the function if you are only allowed to park for a maximum of 1 day.

he range of the function is 0≤y≤1080.

R = {(1, -1), (2, 3), (-2, 4), (4, 6)} Determine whether the following relation R is a function?

here are no ordered pairs that contain the same value of x. Therefore, the relation is a function.

The vertical line test

if a vertical line crosses the graph at more than one point, then the relation is not a function

How can we think of a relation as a collection of values represented as ordered pairs?

where the first element of each pair is related in some manner to the second element of the pair.

Which of the following equations define a relation wherein the value of y is obtained by taking the square of the assigned value of x.

y = x^2