Conditional Relative Frequency

​Day 2

• 8.SP.4 - Relative Frequency

• 8.F.1 - Function or Not a Function

• 8.F.3 - Linear Vs. Nonlinear

• 8.F.5 - Examine Function Graphs

Part / Whole * 100 = %

Whole = One of the specified totals

Conditional Relative Frequency

Part / Whole * 100 = %

Whole = Total of all Totals

Relative Frequency

Relative Frequency (8.SP.4)

​Be careful of key words: OF, WHO and THAT

Multiple Choice

What is the relative frequency that students prefer movies and popcorn?

• 14%

• 42.4%

• 35%

• 13%

Multiple Choice

Of students who prefer movies, what is the relative frequency that prefer popcorn?

• 14%

• 42.4%

• 35%

• 13%

Of students who prefer movies, what is the relative frequency that prefer popcorn?

Conditional Relative Frequency

What is the relative frequency that students prefer movies and popcorn?

Relative Frequency

Relative Frequency (8.SP.4)

​14/108*100 = about 13%

​14/33*100 = about 42.4%

Multiple Choice

Based on the table, what percentage of campers who are 13-16 years old prefer the activity of swimming?

• 30.5%

• 20%

• 12.5%

• 5%

Multiple Choice

What is the approximate relative frequency of students who have a Brand X cell phone?

• 18%

• 35%

• 46%

• 82%

Multiple Choice

Of the children who order a sundae, approximately what percentage get crushed candy?

• 17.1%

• 17.7%

• 27.3%

• 28.2%

• Graph - Does not pass the VLT (Crosses more than once)

• Table - for each input (x) there is more than output (y)

Not a Function

• Graph - Passes the Vertical Line Test (Crosses once)

• Table - for every input (x) there is only one output (y)

Function

Function and Not a Function (8.F.1)

Not a Function

Function

Function and Not a Function (8.F.1)

Multiple Choice

Which table represents a function?

Multiple Choice

Which statement best describes the graph?

• The graph does not represent a function because for every input value, there is only one output value.

• The graph does not represent a function because for some input values, there is more than one output values.

• The graph represents a function because for every input value, there is only one output value.

• The graph represents a function because for some input values, there is more than output value.

Multiple Choice

Which statement is true?

• The graph is a function because for every input, there is exactly one output.

• The graph is a function because for multiple inputs, there is more than one output.

• The graph is not a function because for every input, there is exactly one output.

• The graph is not a function because for multiple inputs, there is more than one output.

Multiple Choice

Which statement describes the graph?

• The graph does not represent a function because for every input value, there is only one output value.

• The graph does not represent a function because for some input values, there is more than one output value.

• The graph represents a function because for every input value, there is only one output value.

• The graph represents a function because for some input values, there is more than one output value.

• Graph - Not a Straight line

• Table - Does not have a Constant Rate of Change (Slope)

• Equation:

  • x is in the denominator

  • x has a power of 2, 3, 4, etc...

  • x is under a square/cube root

  • x is the exponent

  • x is multiplied more than once (this changes the exponent on x)

Nonlinear

• Graph - Straight line

• Table - Constant Rate of Change (Slope)

• Equation:

  • x must have an invisible exponent of 0 or 1 and be in the numerator

​Linear

Linear Vs Nonlinear Functions (8.F.3)

Nonlinear Examples

​Linear Examples

Linear Vs Nonlinear Functions (8.F.3)

Multiple Choice

Which graph is a linear function?

Multiple Select

Select all equations that are linear. Choose two correct answers.

• $$4+y=2x$$

• $$x^2+8=-x$$

• $$2x^2+x=3x-5$$

• $$y-2=2\left(x-5\right)$$

• $$y=2^x$$

Multiple Select

Which two equations represent a nonlinear function?

• $$y=2\left(x-1\right)+1$$

• $$y=2x-1$$

• $$y=\left(x-1\right)^2$$

• $$y=3^x-1$$

• $$y=x-1$$

These problems look a lot alike. Can you tell the difference?

ALERT!

1. Match the Scenario or Graph

or

2. Between x values, what is happening?

Often given as two types of problems:

Examine Function Graphs (8.F.5)

A student leaves home and walks at a constant rate to a friend's apartment before heading to school. The student stops at the friend's apartment for a period of time before continuing the walk at a faster pace.

​

1. Match the Scenario or Graph

​Which graph best represents the distance the student has walked since leaving home?

Multiple Choice

Read the scenario and answer the question.

2. Between x values, what is happening?

Multiple Choice

Which statement is true?

• When x is between -8 and -5, the function is nonlinear and decreasing.

• When x is between -5 and 1, the function is linear and increasing.

• When x is between 1 and 7, the function is linear and increasing.

• When x is between 7 and 9, the function is nonlinear and decreasing.

Multiple Choice

Which statement is true?

• When $$-2<x<1$$ the function is decreasing, and when $$3<x<6$$ the function is decreasing.

• When $$-2<x<1$$ the function is decreasing, and when $$3<x<6$$ the function is increasing.

• When $$-2<x<1$$ the function is increasing, and when $$3<x<6$$ the function is decreasing.

• When $$-2<x<1$$ the function is increasing, and when $$3<x<6$$ the function is increasing.

Draw

Give Lou a hat.