Functions Review

Functions

• There should only be ONE x value for each y value

• On a graph, there should only be one put going down the vertical (y-axis) line

Rate of Change and Initial Value

• Rate of change (slope): Key words-each, per, over time

• m = y - y / x - x

  
  

• Initial value (y-intercept): Key words-initially, beginning, starting point

• y = mx + b; m = slope; b = y-intercept; x & y = ordered pair

Definition

A RELATION is a set of ordered pairs (like the x-and y-coordinates are in a "relationship". In addition, all of the x-coordinates are called the DOMAIN and all of the y-coordinates are called the RANGE.

Example: Name the domain and range for this relation below

(-5, -3), (-2,0), (1,3), (4,6), (7,9)

Domain (all the x-values): {-5, -2, 1, 4, 7}

Range (all the y-values): {-3, 0, 3, 6, 9}

Multiple Choice

Which numbers make up the domain of this relation below:

(7, 5), (-3, 2), (1,- 1), (4, -6), (-2, 4)

• {1, 2, 3, 4, 5}

• { -3, 1, 7}

• {-3, -2, 1, 4, 7}

• {-6, -1, 2, 4, 7}

Functions

A relation can be any kind of relationship between sets of numbers, FUNCTIONs are a special kind of relationship where EVERY INPUT MUST HAVE EXACTLY ONE OUTPUT.

In other words, the x-value cannot repeat

Multiple Choice

Does the relation below a function:

{(–7, 4), (–8, 3), (–7, 7), (–20, 8), (5, 9), (3, 1), (2, 6)}

• Yes

• No

Multiple Choice

Does the relation below represent a function:

{(10, 9), (–2, –16), (–6, 7), (5, 8), (8, –16), (–11, 9)}

• Yes

• No

Does this graph represent a function?

Vertical Line Test

You can easily determine if a relation is a function by graphing it and doing a vertical line test. Just draw a vertical line (or two) on the graph - if your vertical line ever touches two points of the relation, it's not a function. In other words, the vertical line test proves that none of the x-values repeat, and a relation is a function if none of the domain numbers (x-coordinates) repeat.

Examples

Multiple Choice

Is the relation shown in the table a function?

• Yes

• No

You can graph the table too.

If we took the relation from the table and graphed it, this is what it would look like.

Did it pass the vertical line test?

Yes. Therefore, the relation is a function.

Multiple Choice

Is the relation shown in the table a function?

• Yes

• No

Graph the relation given in the table.

Did it pass the vertical line test?

No. Therefore, this relation is not a function.

Multiple Choice

Is this table a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this mapping a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this mapping a function or not a function?

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Distance - Time Graphs

• Linear (straight) line shows moving at a CONSTANT Rate.

• Non-linear (curved) show acceleration or deceleration.

Distance v Time Graphs

• The straight green line sloping upwards show the line is moving away from the starting point at a constant speed.

• The blue line shows 3 parts. Part 1: moving away at a constant speed. Part 2: Stopped (zero slope shows no movement). Part 3: Returning to the starting point at a constant speed.

• The red line is non-linear. It starts 2 seconds later than the other two with acceleration, then deceleration then levels out to a stop (zero slope).

Multiple Choice

Daniel biked to the park. On the way, he stopped for a soda, then continued to the park. After playing a game of catch, Daniel biked home. Between which two points did Daniel more than likely stop for a soda?

• between points B and C

• between points C and D

• between points D and E

• between points E and F

Multiple Choice

The graph shows Nick's bike ride from home to his grandparents and then returning home. Which intervals show Nick's distance from home increasing?

• Interval A and B

• Interval D and F

• Interval C and E

• Interval A, B, C, and E

Multiple Choice

I began to walk; then, I increased my pace and held it constant for a period of time and then decreased my pace slowly. Which graph models this situation?

• A

• B

• C

• D

Poll

Best Gru Meme....

Linear and Non-Linear Functions

Linear Functions...

are straight lines on a graph

Linear Functions...

have a constant rate of change

Linear Functions...

are represented by equations that have:

* no exponents

* no absolute value signs

* fractions with variables only in the numerator

Non-Linear Functions...

have curves or

two or more different slopes

Non-Linear Functions...

do not have a constant rate of change

Nonlinear Functions...

are represented by equations that have:

* exponents

* absolute value signs

* fractions with variables in the denominator

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Linear or Nonlinear?

• Linear

• Nonlinear

Multiple Choice

$$\left|x\ +\ 5\right|\ =\ 43$$  

• Linear

• Nonlinear

Multiple Choice

$$y=x^4$$  

• Linear

• Nonlinear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

$$y\ =\ 6x\ +\ 5$$  

• Linear

• Nonlinear

Multiple Choice

$$y=\frac{6}{x^2}\$$  

• Linear

• Nonlinear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear

• Nonlinear

Multiple Choice

The table represents a function. Is it linear or non-linear?

• Linear

• Nonlinear

Multiple Choice

Is the table linear or nonlinear?

• Linear

• Nonlinear

Poll

Pick the one that speaks to your soul.

• Rainbows and Unicorns, because we can all use some joy in our lives.

• Pizza. I'll say it again. Pizza.

• I blame video games.

• Speak to me in memes, because I don't do words.

• Can we just learn please.

Multiple Select

I am going to do great on my test!!

• Yes!!!

• Yess!

• Yes! Yay!

• Fo Sho!