Topic 3: Got it down so far?

Topic 3: Got it down so far?

3-1: Identifying functions

Functions...

• cannot have repeating x-coordinates

• must pass the vertical line tes

Multiple Choice

Which option is NOT a function?

To determine if something is a function:

• Equations: type into Desmos, perform vertical line test

• Coordinates: look for repeating x-coordinates

• Graphs: perform vertical line test

Multiple Select

Check the statements that are true about this table.

• Function

• Not a function

• Input values are x-coordinates

• Output values are x-coordinates

Multiple Choice

Do these coordinates make a function?

• Yes

• No

Multiple Choice

• Function

• Not a function

Multiple Select

Which of these are a function? Check all that apply

• None of these are functions

• x=5

• $y=x^2-5$

• $y-4=2\left(x+1\right)$

Linear and Nonlinear Functions

Linear Functions

• Made of a straight line

• Have a constant slope

• Data usually held in an XY table or input/output table

Nonlinear Functions

• Curved lines

• Coordinates are held in a domain/range table

• Cannot calculate their slope

Multiple Choice

Which function is linear?

• Function I

• Function II

Multiple Select

What is true about this graph? Check all that apply.

• It is a function.

• It is not a function.

• It is linear

• It is nonlinear

• It has a slope we can calculate

Calculating Slope from a Table

• Usually called rate of change

• Found by finding the change in y over the change in x

• 
  

Multiple Choice

What is the slope of a line with these coordinates?

• $\frac{3}{15}$

• $\frac{1}{5}$

• $5$

• $\frac{12}{1}$

Multiple Choice

Find the slope.

• $-5$

• $5$

• $\frac{1}{5}$

• $-\frac{1}{5}$

Multiple Choice

What is the slope?

• $-1$

• $1$

• $2$

• $-2$

Writing a Linear Equation From a Table

• You need the m and b

• Plug those numbers into the equation y= mx+b

To find m from a table

• Find the slope (rate of change) by finding the change in y over the change in x

• Write your equation so far, with slope in the place of m. y= __x+b

To find the y-intercept from a table

• Pick a random coordinate to plug into the places of x and y

• 
  

Here's a trick!

• If you are given a coordinate on the table in which x is 0, the corresponding y coordinate is b (the y intercept)

• Check out the row in red on the table, when x=0, the y-coordinate is b.

Once you know m & b, plug them into the form y=mx +b

• If m=-2 and b=7, then y=-2x+7

• If m= 1 and b=0, then y=1x + 0

Key concept

Multiple Choice

Which is the correct equation for the table?

• $y=\ 4x\ +\ 3$

• $y=\ \frac{3}{2}x+\ 0$

• $y=\ \frac{2}{3}x\ +\ 3$

• $y=\ 1x\ +\ 0$

Multiple Choice

What is the equation that matches the table?

• $y=\ -2x\ +\ 4$

• $y=\ \frac{1}{2}x\ -\ 4$

• $y=\ -\frac{1}{2}x\ +\ 0$

• $y=\ 4x\ -2$

Multiple Choice

What is the y-intercept of a line with the equation:

 $y=-\frac{1}{3\ }x\ +\ 0$  

• 0

•  $-1$  

•  $-\frac{1}{3}$  

• 3

Multiple Choice

What is the y-intercept of a line with the equation:

 $y=\ 0.7x\ +\ 1$  ?

•  $-1$  

•  $0.7$  

•  $1$  

•  $0.3$  

Multiple Choice

What is the slope of a line with the equation:

 $y=\ -10x\ -\ 5$  

•  $-10$  

•  $-5$  

•  $-15$  

•  $5$  

You will be given word problems than can be modeled by a linear equation

Linear equations are written in the form y=mx + b

Look for keywords to identify slope

• Slope is usually being described as a rate something is changing

• Key words to find slope in a word problem: "average", "earning", "_____ over time", "adds", "increases by"

Multiple Choice

George has $300 in the bank. Each month his bank account increases by $200. What is the slope of this function?

• 300

• 200

• not enough information to tell

In a word problem, the slope will be the number that tells you how things ("variables") are changing.

• The baby ducks grow an average of 10g per week (m= 10)

• The planet warms an average of 1 degree Celsius each year (m= 1)

Multiple Choice

What is the slope of this function? Billie grows fruit in a garden. On average, Billie harvests 24 strawberries per week. After 8 weeks, Billie has an harvested 192 strawberries in total.

• 96

• 192

• 24

• 12

When we find the slope in a word problem, this becomes m in an equation.

• The baby ducks grow an average of 10g per week (m= 10)

• If the slope is 10, the equation will look like y=10x + b

Multiple Choice

Amy is an avid reader. She reads 10 books every year. By the time Amy was 12, she had already read over 900 different books.

• y = 900x + b

• y= 10x + b

• y= 910x + b

So how do we find the b of a linear function when we are given a word problem?

• starting amount, b= that amount

• "time zero" or beginning before any change has happened, b= 0

Multiple Choice

George has $300 in the bank and adds $200 more each month.

What is the b of this equation?

• 200

• 300

Multiple Choice

Billie has 72 strawberries harvested at the beginning of the growing season. She harvests an average of 24 more strawberries per week. At the end of the growing season she has harvested 192 strawberries.

What is the b of this situation?

• 192

• 72

• 24

What we are doing is creating a model for real life linear relationships

When we get a situation in which we can write an equation y=mx + b, we can make predictions about future events.

Multiple Choice

Write the equation that represents the linear function in the situation below.

Henry has 900 XP (experience points) in a video game. He earns about 48 more XP each day that he plays.

• y = 48x + 900

• 900= 48x + b

• y= 900x + 48

Multiple Choice

Professor Doodle wants to make funny math T-shirts and sell them online. Professor Doodle earns $15 for every shirt he sells.

• y = 15x + 0

• y= x + 15

• 15 = 0 + x

We can also look at functions that model real life situations

These functions are usually in quadrant 1, have labels on the y and x axis, and have one or more intervals

Multiple Choice

How many intervals does this graph have?

• 1

• 3

• 5

• 4

Intervals can be:

Increasing

Decreasing

or

Constant

Multiple Choice

Is interval A increasing, decreasing or constant?

• Increasing

• Decreasing

• Constant

Multiple Choice

Is interval B increasing, decreasing or constant?

• Increasing

• Decreasing

• Constant

Multiple Choice

How many decreasing intervals are there?

• One

• Two

• Three

• Zero

One final check to make sure you've got it all down

Multiple Choice

Which option best describes this function?

• Linear

• Nonlinear

Multiple Choice

Is this a function?

• Yes it is a function.

• No it is not a function.

Multiple Choice

What is the slope of this function?

• -2

• 2

• $\frac{1}{2}$

• $-\frac{1}{2}$

Multiple Choice

In the equation y= mx + b, what does m stand for?

• The x-intercept

• The equation of the line

• The y intercept

• The slope

Multiple Choice

What is the slope of the line y= -8x + 9?

• 0

• 9

• -8

• b

Multiple Choice

How many constant intervals are there?

• 1

• 2

• 0

• 4

Multiple Choice

Which option best describes interval A?

• Increase

• Decrease

• Constant

Multiple Choice

Which option best describes interval E?

• Increase

• Decrease

• Constant

Multiple Choice

If a person starts 5 miles from home and they continue driving at a rate of 50 miles per hour away from home, what does the equation of this function look like?

• y= 50x + 5

• y= 5x+50

• 50=5m+b

The end!

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