Introduction to Functions

Warm Up Structure

The quiz isn't a grade--just a tool to help me see how well you understand the topic. The warm ups themselves will still be a grade.

The rest of the week you need to be working on the rest of the pages, using the notes as a reference.

​

​At the end of the week there will be a small quiz over the warm up topic to see how well you've mastered it

​At the start of the week we take notes

Mod 6--Linear Functions

Skills Review

• ​Slope

• ​Y-intercept

• ​Graphing Equations/points

• ​Analyzing Equations and graphs

New Skills

• Quantitative descriptions (both verbal and graphically)

• Scatter Plots

• ​Frequency Analysis

Formula Quiz

Starting next week, we will have a formula quiz every week on Fridays

Vocabulary

​Some text here about the topic of discussion.

• ​Thursday Jan 13th

• ​Thursday Jan 20th

• ​Thursday Jan 27th

We will have vocab tests on:

Mod 6 Vocab

Code: 0236 3593​

Association

a relationship between the two variables of a bivariate data set

Bivariate Data Set

An ordered list of ordered pairs of data values (called data points). Data values can be either numerical or categorical.

Column Relative Frequency

Cell frequency divided by the column total for that cell.

Linear

Relation that makes a straight line

Nonlinear

Relation that does not make a straight line

Row Relative Frequency

The number given by dividing the cell frequency by the row total for that cell

Scatter Plot

Graph of a numerical bivariate data set.

Slope

How steep a line is;

​

Can be found by dividing the vertical change by the horizontal change​

Two Way Frequency Table

A rectangular table used to summarize data on two categorical variables of a bivariate data set. The rows of the table correspond to the possible categories for one of the variables, and the columns correspond to the possible categories for the other variable. Entries in the cells of the table indicate the number of times that a particular category combination occurs in the data set; the value is the frequency for that combination

y-intercept

Where a line crosses the y-axis; the initial value

Function Review

Multiple Choice

• Function

• Not a Function

Multiple Choice

The following is not a function because...

• There are two values that equal 2.

• x = 10 and x = 40 has two values each.

• In the f(x) column, the 5 repeats.

• This table is actually a function.

Multiple Choice

Which set of ordered pairs is a function?

• {(9,5), (10,5), (9,-5), (10,-5)}

• {(3,4), (4,-3), (7,4), (3, 8)}

• {(6,-5), (7, -3), (8, -1), (9, 1)}

• {(2, -2), (5, 9), (5, -7), (1, 4)}

Some text here about topic of discussion

Slope and y-intercept

Slope

Topics in this quizizz:

- Identifying slope (direction)

- Finding slope of a line (steepness)

- Slope from a Table

- Slope from an Equation

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

Multiple Choice

What type of slope?

• positive

• negative

• zero

• undefined

Multiple Choice

What type of slope?

• negative
• steep
• undefined
• zero slope

Multiple Choice

What type of slope?

• zero slope
• undefined
• negative
• positive

Multiple Choice

What type of slope?

• undefined
• positive slope
• negative slope
• zero slope

Finding the Slope of a Line

• Slope can tell us how steep a line is!

• Each line can be assigned a value (a #) that tells us how steep the line is.

• Slope is written as a ratio (rise/run)

• Always make sure to simplify your answer!

Finding the Slope of a Line

• Slope can tell us how steep a line is!

• Each line can be assigned a value (a #) that tells us how steep the line is.

• Slope is written as a ratio (rise/run)

• Always make sure to simplify your answer!

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

• 3

• $$\frac{1}{3}$$

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{2}{1}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• 3

• $$\frac{1}{3}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{5}{3}$$  

• $$\frac{3}{5}$$  

• 5

• $$\frac{5}{4}$$  

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{4}{2}$$  

• 2

• 3

• $$\frac{2}{3}$$  

Finding slope from a Table

• Slope = change in y/change in x

• Use the table to find the value the y is changing by. That is the numerator!

• Use the table to find the value the x is changing by. That is the denominator!

• ANOTHER OPTION: Graph the points and count rise/run

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$2\ \frac{1}{2}$$

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{1}{2}$$  

• $$\frac{4}{8}$$  

• 4

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• 3

•   $$\frac{1}{3}$$  

• $$-\frac{1}{3}$$  

• -3

Slope from an equation

• The number in front of the x in the equation is the slope!

Multiple Choice

Identify the slope in the equation:

$$y=8x$$  

• 8

• 1/8

• -8

• 0

Multiple Choice

Identify the slope in the equation:

$$y=\frac{5}{6}x$$  

• $$\frac{5}{6}$$  

• $$\frac{6}{5}$$  

• 5

• 6

Review of semester 1 skills--quizizz questions

What is a Translation

A rigid motion transformation that moves every point of one figure the same amount and preserves the orientation. 

What is a Reflection

A type of transformation where every point is mapped across a line. The original point and the new point are equidistant from the line. 

What is a Reflection Line?

a line that acts as a mirror so that corresponding points are the same distance from the mirror

Multiple Choice

Which statement describes the move from frame 1 to Frame 2?

• Rotate right

• Translate up

• Reflect vertically

• Translate down

Multiple Choice

Identify the type of transformation that is being performed here.

• Translation

• Reflection

• Dilation

• Rotation

Multiple Choice

The pre-image is_________________

• the figure before the transformation

• the figure after the transformation

• the figure with prime points

• the second figure

Multiple Choice

Describe the Transformation

• Reflection
• Translation
• Rotation

Multiple Choice

What Transformation is visible?

• Dilation
• Refection
• Translation
• Rotation

Multiple Choice

Name the transformation.

• Translation
• Reflection
• Rotation

Multiple Choice

Describe the transformation in the image

• Translation

• Reflection

• Rotation

What are the parts of a power?

When you MULTIPLY 2 terms with the SAME BASE, ADD their exponents.

When you MULTIPLY 2 terms with the SAME BASE, ADD their exponents.

Multiple Choice

Simplify the expression

$$x^5\cdot x^7$$  

• x³⁵

• x¹²

• x²

• x^-2

Multiple Choice

Simplify

$$2^4\cdot2^5$$  

• 2²⁰

• 4⁹

• 4²⁰

• 2⁹

When you DIVIDE 2 terms with the SAME BASE, SUBTRACT their exponents.

When you DIVIDE 2 terms with the SAME BASE, SUBTRACT their exponents.

Multiple Choice

• 1¹⁰
• 1²⁶
• z¹⁰
• z²⁶

Multiple Choice

• 4³

• 4¹⁵

• 1³

• 1¹⁵

Multiple Choice

If the exponent on your power of 10 is positive, is your number larger or smaller than 10?

• Larger
• Smaller

Multiple Choice

7.82 x 10^-6 is an example of scientific notation. The exponent of -6 tells you your number will be very ________.

• Large
• Small
• Basic

Multiple Choice

Change from standard form to scientific notation: 12,000,000

• 12.0  x  10⁷
• 0.12  x  10⁷
• 1.2  x  10⁶
• 1.2  x  10⁷

Multiple Choice

Change from standard form to scientific notation:  450,000

• 4.5  x  10⁵
• 45  x  10⁵
• 4.5  x  10⁴
• 4.5  x  10⁶

Multiple Choice

Change from standard form to scientific notation:  0.000398

• 39.8  x  10^-5
• 3.98  x  10^-5
• 3.98  x  10^-4
• 39.8  x  10^-6

Multiple Choice

Change from standard form to scientific notation: 0.004078

• 4.078  x  10^-3
• 4.078  x  10³
• 40.78  x  10^-4
• .4078  x  10^-2

Multiple Choice

125,678,000: Change to scientific notation

• 1.25678  x  10¹²
• .125678  x  10^-9
• 12.5678  x  10⁸
• 1.25678  x  10⁸

Multiple Choice

Try to change the number back to standard form:  6.79  x  10⁴

• 679,000
• 6,790
• 67,900
• 6,790,000

Multiple Choice

Try to change the number back to standard form: 3.97  x  10^-2

• 0.000397
• 0.0397
• 0.0000397
• 0.397

Multiple Choice

The factor multiplied by a power of 10 in scientific notation needs to be greater than or equal to one but less than ___________?

• 1
• 10
• 100
• 1,000