8.16 Functions, Slope, and Independent vs Dependent Variables

Functions

Today's Objective: I can determine if a relation is a function

Functions

• When the x that you try gives you only one y THAT'S A FUNCTION

• A function is a special relation where each x-value only has one y-value

When you put an input into a machine you can only get out one input.

THAT'S A FUNCTION!

(Each input has only one output)

These are all functions

EACH X VALUE

HAS ONLY ONE Y VALUE

These are NOT functions

In each example

there is an X VALUE that has more than one Y VALUE

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values paired with it.

• Yes, because each x-value has only one y-value paired with it.

• No, because the x-value 11 has two y-values paired with it.

• No, because each x-value has only one y-value paired with it.

Multiple Choice

Is this table a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this mapping a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this set of ordered pairs a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this set of ordered pairs a function or not a function?

• Function

• Not a Function

The vertical line test

• To tell if a graph is a function, draw a vertical line anywhere on the graph.

• If any vertical line touches the graph in more than one location it is NOT a function

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1

• Graph 2

• Graph 3

• Graph 4

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Slope Intercept Form

Writing and Graphing Equations Using y=mx+b

Multiple Choice

Which of these represents slope-intercept form?

• y - y₁ = m(x-x₁)
• Ax + By = C
• y = mx + b

Multiple Choice

Determine the slope and y-intercept from the following equation:   y = 3/2x + 3

• slope: 5   y-intercept:  (0,3) 
• slope: 3/2   y-intercept:  (0,3) 
• slope:  4  y-intercept:  (0,3/2)
• slope: 1/5   y-intercept:  (0,5) 

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6
• y=3x-6
• y=3x+6
• y=6x+3

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3
• y=2/3-3
• y=2/3x-3
• y=2/3x+3

Multiple Choice

What is the y-intercept in the following equation:  y=-4x-5

• -4
• -4x
• 5
• -5

Multiple Choice

What is the slope in the equation:  y=4x+3

• 3
• 4x
• 4
• x

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• nothing

Multiple Choice

What is the equation of a line when m = -7 and b = -8?

• y = -7x + 8

• y = -7x - 8

• y = 7x - 8

• y = 7x + 8

Multiple Choice

What is the y-intercept of the line?

• (0,-3)

• (-3,0)

• (4,0)

• (0,4)

Correct Answer

y-axis goes up and down.

Multiple Choice

Same graph, what is the slope?

• $$\frac{3}{4}$$

• $$\frac{4}{3}$$

• $$-\frac{3}{4}$$

• $$-\frac{4}{3}$$

Pick two points.
Count Up or Down (3 up)
Count Left or Right (4 right)

3 is the top number
4 is the bottom number

The line goes UP from LEFT to RIGHT so we know the slope is positive.

Slope Intercept Form

The number before the x is the slope.

The number after the x is the

y-intercept.

Multiple Select

Given:  $$y=-\frac{1}{3}x+5$$ , find the slope and y-intercept.

• Slope:  $$-\frac{1}{3}$$  

• y-intercept:  $$5$$  

• Slope:  $$5$$  

• y-intercept:  $$-\frac{1}{3}$$  

• Slope:  $$-\frac{1}{5}$$  

Multiple Select

Given:  $$y=-5x+3$$ , find the slope and y-intercept.

• Slope:  $$-5$$  

• y-intercept:  $$3$$  

• Slope:  $$5$$  

• y-intercept:  $$-3$$  

• Slope:  $$-\frac{1}{5}$$  

Multiple Select

Given:  $$y=\frac{3}{5}x$$ , find the slope and y-intercept.

• Slope:  $$\frac{3}{5}$$  

• y-intercept:  $$0$$  

• Slope:  $$1$$  

• y-intercept:  $$1$$  

• y-intercept:  $$\frac{3}{5}$$  

Multiple Choice

Which graph represents the function:   $$y=-\frac{1}{2}x-2$$  

Multiple Choice

Which graph represents the function:   $$y=\frac{3}{2}x+3$$  

Multiple Choice

Which graph represents the function:   $$y=x+3$$  

Multiple Choice

Which equation matches the graph?

• y= 0.5x - 5
• y= -0.5x - 5
• y= 0.5x + 5
• y= -0.5x + 5

Multiple Choice

Which equation matches the graph?

• y= 3x - 5
• y= -3x - 5
• y= 3x + 5
• y= 3x + 5

Multiple Choice

Which equation matches the graph?

• y= 3x - 5
• y= -3x - 5
• y= 3x + 5
• y= 3x + 5

Multiple Choice

Which equation matches the graph?

• y= 1x + 3
• y= 1x
• y= -1x + 3
• y= -1x

Multiple Choice

Which equation matches the graph?

• y= 1x + 3
• y= 1x
• y= -1x + 3
• y= -1x

Multiple Choice

Which equation matches the graph?

• y= 2x + 5
• y= 2x
• y= -2x + 5
• y= -2x

Multiple Choice

Which equation matches the graph?

• y= 2x + 5
• y= 2x
• y= -2x + 5
• y= -2x

Dependent Variable vs Independent Variables

Example:

Sarah is participating in a walkathon to raise money for local literacy programs. The amount of money Sarah will raise depends on the distance she walks.

m = the amount of money Sarah will raise (DEPENDENT)

d = the distance Sarah walks (INDEPENDENT)

Multiple Choice

Maggie opened a savings account and deposited $200. She will deposit $50 into this account each week, w, and will make no withdrawals. The equation below shows how she will calculate the total amount in the account, t, after each deposit.

Which of the following is the dependent variable? $$t=50w+200$$  

• $$t$$  

• $50

• $$w$$  

• $200

Multiple Choice

Identify the dependent variable:

The cost of apples (c), and the number of pounds you buy (p)

• p = dependent

• c = dependent

Multiple Choice

Name the DEPENDENT variable from the table below.

• minutes

• bubbles

Multiple Choice

Name the INDEPENDENT variable from the table below.

• words

• minutes

Multiple Choice

Carey and Justin are raising money to purchase books for their school's library. The more money they raise, the more books they will be able to purchase for the library.

m = the amount of money Carey and Justin raise

b = the number of books Carey and Justin will be able to purchase

Which of the variables is dependent?

• m

• b

Multiple Choice

Sarah is bringing treats to her elementary school class on her birthday. The number of treats she brings in is based on the number of students in her class.

t = the number of treats

s = the number of students

Which of the variables is independent?

• s

• t

Multiple Choice

Sophie earned $1 for every she got an A on her report card.

m = money

A = A on report card

The dependent variable is:

• m = money

• A = A on report card

Multiple Choice

A movie ticket is $8.50 per person. What is the independent variable?

• Cost

• Number of people

• Time

• Cinema