Lesson 118-122

Why didn’t the quarter roll down the hill with the nickel?

Lessons 118-122

Cassi Riggs

May 8, 2023

Lesson 118- Relations & Functions

Two-Variable Equations

Example: y=3x

TT gives us a scenario of water flowing from a hose. In this equation x=hours and y=amount of water. We can find our either the hours or amount of water depending on what we already know. If we know how many hours we can solve for amount of water and vice versa.

The technical definition of a function is a relationship between variables where if you pick a value for x, there’s just one matching value for y.

A relation is any relationship between variables. So a function is a special kind of relation—one where each x-value has just one matching y-value.

Multiple Choice

A relation is a relationship between two variables such as x and y.

• True

• False

Multiple Choice

A function is a special kind of relation where if you pick a value for x, there’s just one matching value for y.

• True

• False

Multiple Choice

The equation y=60x represents a function.

• True

• False

Multiple Choice

Is this a function?

• Yes

• No

Multiple Choice

Is this a function?

• Yes

• No

Multiple Choice

For the function y=4x+7, find the matching y-value when x=3.

• 19

• 15

• 5

• 8

Lesson 119- More on Functions

Dependent & Independent Variables

y=7x+3

The dependent variable is the y because it depends on whatever you put in for x.

x is independent

The range is all the possible numbers that the dependent variable can equal.

Range

The domain of a function consists of all the numbers that can possibly be put in for x, the independent variable.

Domain

Some Key Terms

Any real number except 0, because there is no way to make the numerator equal 0

Range

Any number except 2, because the denominator can not equal 0

​Domain

Multiple Choice

$$y=\frac{8}{x-3}$$ What is the domain and range of this function?

• Domain: All real numbers except 3; Range: All real numbers except 8

• Domain: All real numbers except 3; Range: All real numbers except 0

• Domain: All real numbers except 0; Range: All real numbers except 8

• Domain: All real numbers except 8; Range: All real numbers except 0

Multiple Choice

In a function, the variable that’s by itself on one side is the dependent variable, and the other variable is the independent variable.

• True

• False

Multiple Choice

The domain of a function is all the numbers that you could possibly put in for the independent variable.

• True

• False

Multiple Choice

The range of a function is all the numbers that make a denominator equal to 0.

• True

• False

Multiple Choice

Can a fraction have a denominator of zero?

• Yes

• No

Lesson 120- Functional Notation

y(x) means "y of x"

This is just a shorter way of writing the function.

Notation is a fancy way of saying to write something :)

Solve

Multiple Choice

If y=4x-3, find y(7).

• 25

• 24

• 31

• 28

Multiple Choice

Functional notation is a short way of writing functions.

• True

• False

Multiple Choice

Functional notation makes it easy to see what number you’ve put in for the independent variable.

• True

• False

Lesson 121- The Coordinate Plane

Graphing Functions

The image here is called a coordinate plan.

There is an x-axis and y-axis.

We can take function equations and put them on the coordinate plan. We start with x and then plot y.

Quadrants

Multiple Choice

What quadrant is point A in?

• I

• II

• III

• IV

Multiple Choice

Tell the coordinates of point F shown below.

• (-6,3)

• (-3, 6)

• (3,-6)

• (6,-3)

Multiple Choice

Tell the coordinates of point E shown below.

• (-4,1)

• (4,-1)

• (-1,4)

• (1,-4)

Multiple Choice

On a coordinate plane, any two numbers, such as x = 2 and y = 5 can be turned into a point.

• True

• False

Multiple Choice

In an ordered pair, the y-coordinate is always listed first and the x-coordinate is always listed second.

• True

• False

Lesson 122- Graphing Equations

Multiple Choice

Select the graph of the function $$y=-3x+1$$

Multiple Choice

A coordinate plane can be used to graph (draw a picture of) a function.

• True

• False

Multiple Choice

A graph is created by turning pairs of x and y values into points on the coordinate plane and drawing through the points according to the pattern.

• True

• False

Homework

• Lessons 118-122 in TT App

• Chapter 15 Vocabulary