Unit 1 Reteach

Unit 1 Reteach

Linear Inverse

• Switch x and y

• Solve for y (rewrite as y=mx+b)

Example

Multiple Choice

Find the inverse of

 $f\left(x\right)=4x+5$  

•  $y=x-\frac{5}{4}$  

•  $y=5x+4$  

•  $y=\frac{x-5}{4}$  

Function Composition

• Substitute a number into an equation

Fill in the Blank

Find $f\left(g\left(2\right)\right)$  for  $f\left(x\right)=x+2$  and  $g\left(x\right)=3x$ . 

What number should you plug in first?

Multiple Choice

Find $f\left(g\left(2\right)\right)$  for  $f\left(x\right)=x+2$  and  $g\left(x\right)=3x$ . 

Are you going to plug in 2 to the f equation or the g equation?

• f

• g

Multiple Choice

Find $f\left(g\left(2\right)\right)$  for  $f\left(x\right)=x+2$  and  $g\left(x\right)=3x$ 

• 12

• 2

• 8

Proving Inverse with Composition

• Plug an equation into another equation

•  $f\left(g\left(x\right)\right)=x$  and  $g\left(f\left(x\right)\right)=x$  

 $f\left(x\right)=-\frac{1}{4}x-\frac{9}{4}$             $g\left(x\right)=-4x-9$  

Multiple Choice

What is $f\left(f^{-1}\left(5\right)\right)$ ? 

**Remember that inverses undo each other. 

• 5

• -1

Domain and Range of a Piecewise Function

• domain: left to right

• range bottom to top

• Parenthesis for infinity or open circle

• Everything else is a bracket

Multiple Select

What is the domain.

**There are 2 correct answers

•  $\left(-\infty,3\right)$  

•  $\left(-6,1\right)$  

•  $x<3$  

•  $\left(-6,3\right]$  

Linear Regression

• desmos.com

• enter the table

• y₁~mx₁+b

• m is slope

• b is y-intercept

Fill in the Blank

What is the y-intercept?
x        y
2        7
4       5
6       4
8       2
10      1

Multiple Choice

Is the slope positive or negative?

x        y
2        7
4       5
6       4
8       2
10      1

• Positive

• Negative

Poll

Do you feel ready to answer these questions on the retest tomorrow?

• 1 - No 💙

• 2 - I need a little more help

• 3 - YES!