Algebra chapter 3 interactive review

​Per 1

Mrs Thompson​

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(Doesn't HAVE to be a function) (But it could be one)

This is an example of a relation​

A collection of ordered pairs containing one

object from each set​

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​A relation is...

Gizelle Du. made this one!​

Draw

Can you draw something that would be a function?

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This is an example of a function

A relation or expression involving 1 or more variables

(One input/x value only!)​

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​A function is...

Kailani helped with this one!! (not just this one, a lot more)​

Multiple Choice

Quick! Which one of these questions represents a function?

• 5,0

  3,2

  3,2

  1,2

• 6,3

  2,3

  4,3

  1,3

• 2,1

  2,5

  3,1

  0,7

• 3,7

  8,9

  3,4

  6,1

Multiple Select

Quick! Select all that applies to a relation

• ITS ALWAYS A FUNCTION!!

• ITS A RELATION!!!

• IT CAN BE NOT A FUNCTION & A FUNCTION!!!!

• I DON'T REMEMBER!!! HOW SHOULD I KNOW??

• ITS NEVER A FUNCTION!!! $$\lim_{x\rightarrow y}$$  

Domain is blue

Range is red​

(5,1) (2,3) (5,4) (0,1)​

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Domain & range!

X values​

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Y values​

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Multiple Choice

Whats a independent variable?

(Don't pick the arrows. It will be wrong.)

• $$\rightarrow$$  

• A VARIABLE THAT DEPENDS ON SOMETHING

• A VARIABLE THAT DOESN'T DEPEND ON SOMETHING

• $$\leftarrow$$  

Independent - It's variation doesn't depend on another

Dependent - It's variation depends on another

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Dependent & Independent

X values​

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Y values​

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​(Variables)

Example :​

y = 4x + 8h

Multiple Choice

Whats a dependent variable?

(Don't pick the arrows. It will be wrong.)

• $$\rightarrow$$  

• A VARIABLE THAT DEPENDS ON SOMETHING

• A VARIABLE THAT DOESN'T DEPEND ON SOMETHING

• $$\leftarrow$$  

X intercept - When a line crosses the x axis

Y intercept - When a line crosses the y axis​

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​Some text here about the topic of discussion.

​Intercepts!

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Draw

Circle/put a point on a x intercept

Draw

Circle/put a point on a y intercept

Going up

Increasing​

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Going down

Decreasing​

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Staying the same

Constant

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(Read it from

left to right)

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This is an example of a function

The behavior of the graph of the function as x approaches positive/negative infinity​

​End Behavior is...

Did you guess correctly? If not, don't worry! It's a game so you can review after all!!​

Multiple Choice

True or false

If X approaches infinity, Y most likely approaches infinity as well

• TRUE!! WHO DOESN'T KNOW THIS??

• OBVIOUSLY FALSE!! NEXT QUESTIONN!!

Open Ended

In your own words, what is end behavior?

An equation written a form similar to 1x+3y+4=0

(coefficients do NOT = 0)

(1,3, and 4 are random #s)​

Transformaation

Did you guess correctly? If not, don't worry! It's a game so you can review after all!!​

​For example

5x+3y=30​

5x+3(0)=30

x=6​

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Some text here about the topic of discussion

5(0)+3y=30

x=10

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Multiple Choice

WHATS A VARIABLE??

• THE LETTER THINGYS

• THE NUMBER THINGYS

• THE COEFFICIENT THINGY!

• THE ANSWER

  (this is not the answer.. or is it?)

​Nonlinear & Linear

​(Functions)

Linear - Graph is a straight line

Nonlinear - Graph is crooked/not straight

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Draw

Draw both a nonlinear and linear function Use different colors!

​Discrete VS Continuous

​Discrete - points on a graph that only has specific numbers

Continuous - Consists of all numbers in an interval​

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​Domain

Draw

QUICK! DRAW A CONTINUOUS DOMAIN!

​Function Notation

​Function notation- Easy way to write and understand functions.

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Open Ended

Whats an example of a function notation?

Poll

Do function notations REALLY help you learn?

• honestly no

• honestly yes

• honestly it doesn't make a difference

​Standard Form

​Standard form- A way of writing down numbers easily

625 = 600+20+5​

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​(In algebra)

​(Elementary)

Multiple Select

Select the constants in

Ax + By = C

(all that applies)

• A

• X

• B

• Y

• C

​Slope

Slope:

Rate of change between two points on a line

Multiple Select

Slope is equal to...

Mark all that applies

• RISE!!!

• POSITIVE!!

• RUN!!

• NEGATIVE!!!

• CONSTANT!!! AND NOT SO CONSTANT!!

Rise - How many units you move up or down from point to point

RUN! - How far left from right you move from point to point

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​Rise over RUN!

X values​

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Y values​

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Example :​ ​5/8

Go up 5 Go right 8​

​Negatives:

Left, down​

Multiple Select

$$\frac{2}{3}$$   

What do we do here?

• GO UP!!!

• GO DOWN!!

• GO LEFT!!!

• GO RIGHT!!!!

• GO BOTH WAYS!!!

  (I don't know)

Slope intercept form - A specific form of linear equations.​

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​Slope--Intercept Form

Structure here :​

y = mx + b​

• Slope

• Y intercept

Same energy as:​

y = 3/4x + 1​

y = ​3/4x + 1

​Starting point: 0,1

Go up 3, Go right 4​

Draw

Draw a slope intercept. Structure: y=2/3+1

​Constant function

Slope intercept form - a function that has the same output value no matter what your input value is

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Family of functions - A set of functions whos equations have similar forms

Parent functions - Simplest form of a given family of functions.

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​Family of functions

Parent functions

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​Family of functions & Parent functions

Multiple Choice

QUICK! Which is apart of the family functions?

• Constant

• Quadrant

• Coefficient

• Parent no function

Transformation - Manipulating a function by adding, subtracting, multiplying or dividing.

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​Transformation

​Translation & Reflection

_{Translation - Make written expressions and equations into numerical form}

_{Reflection -​ Flips a graph over the y axis}

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​Translation

​Horizontal

Shrink & Stretch

_{Horizontal Stretch - Constant is between 0-1}

_{Horizontal Shrink - Squeeze the graph towards the X axis}

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Open Ended

Define horizontal stretch and horizontal shrink

​Vertical

Shrink & Stretch

_{Horizontal Stretch - Constant is greater than 1}

_{Horizontal Shrink - Squeeze the graph towards the X axis}

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Draw

Try drawing a vertical shrink line

Absolute Value Function

_{Absolute value function :}

_{A function that contains an algebraic expression within absolute value symbols such as 3|x+2|}​

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Draw

Write an absolute value function

​Vertex & Vertex form

_{Vertex - Point where the parabola crosses the axis of symmetry}

_{Vertex Form -​ f(x) = a(x – h)2 + k}

_{where a, h, and k are constants. of the parabola is at (h, k).​}

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Multiple Select

How do you find a vertex?

Select all that applies

• With parabola

• With Pentagontal

• With symmetry

• Checking if its perpendicular

• Using a protractor