Unit 2 Understanding Functions IM1 SS

Unit 2

Understanding Functions

IM1 Summer School Sem. 1

Replace this with a sub-header that can be in multiple lines. ​

Match

Match the following to make an explicit equation and identify the cost for 8 passengers

• 75

• 25

• $$a_n=75+25\left(n-1\right)$$

• $$75+25\left(8-1\right)$$

  $$75+25\left(7\right)$$

  $$75+175=250$$

The first term

The common difference

Create the explicit equation

The cost for 8 passengers

• The first term

• The common difference

• Create the explicit equation

• The cost for 8 passengers

Multiple Choice

What is the slope of this line?

• 0

• undefined

• -2

• -1

Multiple Choice

Find the slope of the line

(draw the triangle, label rise and run)

• 2

• 1/2

• -2

• -1/2

To find the slope between the given two points...

Multiple Choice

To find the slope between the given 2 points, first label them:

(-4,1) and (-4,5)

• $$x_1=-4\ and\ y_1=-1$$ $$x_{2\ }=-4\ and\ y_2=5$$

• $$x_1=-4\ and\ x_2=-1$$ $$y_1=-4\ and\ y_2=5$$

Multiple Choice

Now that they are labeled, plug them in to the formula:

(-4,1) and (-4,5)

• $$\frac{\left(5\right)-\left(-1\right)}{\left(-4\right)-\left(-4\right)}$$

• 
  $$\frac{\left(-4\right)-\left(-4\right)}{\left(5\right)-\left(-1\right)}$$

Multiple Choice

Now that they are plugged in, what is the slope?

(-4,1) and (-4,5)

• m=0, it is a horizontal line

• 
  m= $$\frac{-6}{-8}=\frac{3}{4}$$

• m is undefined, it is a vertical line

• m= $$\frac{-8}{-6}=\frac{4}{3}$$

Drag and Drop

The equation of a line with the slope -4 and the y-intercept (0,7) requires me to use the slope intercept form, ​

Placeholder

, and then plug in m which = ​

Placeholder

and b which = ​

Placeholder

to make the equation ​

Placeholder

Drag these tiles and drop them in the correct blank above

y=mx+b

-4

7

y=-4x+7

Multiple Choice

The best equation to use when looking at a graph is...

• Standard

  $$Ax+By=C$$

• Point Slope

  $$\left(y-y_1\right)=m\left(x-x_1\right)$$

• Slope Intercept

  $$y=mx+b$$

Multiple Choice

The best equation to use when looking at a graph requires you to find the y intercept which is...

• 7

• 4

• 0

• -5

Multiple Choice

The best equation to use when looking at a graph also requires you to find the slope which is...

• $$\frac{12}{-4}=-3$$

• $$\frac{12}{4}=3$$

• $$\frac{4}{12}=\frac{1}{3}$$

• $$\frac{4}{-12}=-\frac{1}{3}$$

Multiple Choice

The equation for this graph is

• $$y=\frac{1}{3}x-5$$

• $$y=\frac{1}{3}x-5$$

• $$y=3x-5$$

• $$y=4x-5$$

Dropdown

To find the equation of the line for $$\left(4,-3\right):m=-2$$ you must start with the slope intercept form ​

Select answer

then plug in x,y and m like ​

Select answer

and then multiply ​

Select answer

and solve for ​

Select answer

. Finally, plug in your m and b and you get ​

Select answer

Graphing

Graph the equation:

$$y=\frac{2}{3\ }x-2$$

Multiple Choice

Which of the following is NOT an ordered pair for this line?

• (0,-2)

• (3,0)

• (6,2)

• (-2,0)

Reorder

Reorder the following so you can change a standard equations to slope intercept form to graph it:

• Identify that $$x+2y=10$$ is standard form

• Zero out the x term, $$2y=-x+10$$

• Divide by the coefficient, $$y=-\frac{1}{2\ }x+5$$

• Identify the $$m=-\frac{1}{2}\ and\ b=5$$

• Finally, you can easily graph

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Match

Match the following to show you know the parts of the explicit formula for this formula $$a_n=a_1+d\left(n-1\right)$$

• $$a_n$$ $$or\ f\left(n\right)$$

• n

• d

• $$a_1$$

• $$\left(n-1\right)$$

The nth term

The number of the term

common difference

1st term

Previous term

• The nth term

• The number of the term

• common difference

• 1st term

• Previous term

Match

Match the following to show you know the parts of the recursive formula:

$$a_1=$$

$$a_n=a_{\left(n-1\right)}+d$$

• $$a_n$$

• $$a_{\left(n-1\right)}$$

• $$d$$

• $$a_1$$

the nth term

The previous term

the common difference

The first term

• the nth term

• The previous term

• the common difference

• The first term

Match

Match the following

Identify the parts of the arithmetic sequence

$$\left(35,32,29,26...\right)$$

• It is or is not arithmetic

• Common difference

• 1st term

• 5th term

IS

-3

35

23

• IS

• -3

• 35

• 23

Dropdown

A sequence can be generated using $$a_n=a_{\left(n-1\right)}+10\ where\ a_1=23$$

The first 5 terms are: The first term is ​

Select answer

then I add ​

Select answer

to get the next term which is ​

Select answer

then I add 10 to get the 3rd term which is ​

Select answer

and the 4th term is ​ ​

Select answer

Multiple Choice

The 81st term of the $$a_n=2n+5\ is$$

• 81

• 162

• 167

• 172

Match

Find the explicit formula for 72,76,80,84,...

• first term is

• common difference is

• $$a_n=a_1+d\left(n-1\right)$$

• $$a_n=72+4\left(n-1\right)$$

72

+4

The explicit formula

The explicit formula filled i

• 72

• +4

• The explicit formula

• The explicit formula filled i

Match

Find the recursive formula for 72,76,80,84,...

• first term is

• common difference is

• $$a_1=$$

  $$a_n=a_{\left(n-1\right)}+d$$

• $$a_1=72$$

  $$a_n=a_{\left(n-1\right)}+4$$

72

4

The recursive formula

The recursive formula plugged in

• 72

• 4

• The recursive formula

• The recursive formula plugged in