Math with Michelle- Functions

Math with Michelle- Functions

A function is a relation between 2 variables

each value of x is associated to a value of y

In order to be considered a function

for each value of the independent variable (x) there can only be one value for the dependent variable (y)

Multiple Choice

Independent variable

• x

• y

Multiple Choice

Which value is represented on the horizontal axis? (blue line)

• x

• y

Multiple Choice

Dependent variable

• x

• y

Multiple Choice

Which axis it the y axis?

• horizontal (blue line)

• vertical (purple line)

Multiple Choice

What is the scale of each axis?

• x axis: 2 boxes represents 1 min

  y axis: 4 boxes represent 10ºC

• x axis: 4 boxes represents 1 min

  y axis: 2 boxes represent 10ºC

• x axis: 2 boxes represents 10ºC

  y axis: 4 boxes represent 1 min

Multiple Choice

• function

• not a function

Multiple Choice

• function

• not a function

Multiple Choice

• function

• not a function

Multiple Choice

• function

• not a function

Function variations

Functions can be ^increasing or _decreasing

Many functions have increasing intervals and decreasing intervals

^Increasing function

When independent variable (x) increases, the dependent variable (y) also increases

_Decreasing function

when x ^increases, y _decreases

A function with both increasing and decreasing intervals

Fill in the Blanks

The graph shows the trend of a boys weight between the ages of 2 and 20 years

Complete the following table:

Age (years): 2 | 8 | 14| 20 |

weight(kg): __|__|__|__|

Multiple Choice

This is an example of a(n):

• increasing function

• decreasing function

Multiple Choice

Specify in which of these time periods his weight increased the most:

• Between the ages of 2 and 8

• Between the ages of 8 and 14

• Between the ages of 14 and 20

The function is ^increasing, because weight increases as age increases.

Between 14 and 20 years his weight increased by 26 kg

Company's profits

Study the trend of the company's profits over a few years represented on this graph

Fill in the Blanks

Complete the table:

Multiple Choice

This is an example of a(n):

• increasing function

• decreasing function

The function is decreasing because profits (y) are decreasing as years (x) increase

Multiple Select

Which answer(s) represent the increasing intervals on this graph?

• from 0 to 3

• from 3 to 5

• from 5 to 9

What is the decreasing interval?

What is the decreasing interval?

From 3 to 5

Multiple Choice

Which answer(s) represent the decreasing intervals on this graph?

• from 0 to 3

• from 3 to 5

• from 0 to 5

• from 5 to 11

What is the increasing interval?

What is the increasing interval?

From 5 to 11

Multiple Choice

The interval 0-3 represents:

• the increasing interval

• decreasing interval

What does the interval 3 to 6 represent?

What does the interval 3 to 6 represent?

The decreasing interval

Multiple Select

Which of these graphs have both increasing and decreasing intervals?

• Test average

• Mac & Cheese Consumed

• Time spent crying in class

• Naps

Multiple Choice

The x axis on this graph represents the year in school. What would be a logical variable for the y axis?

• Time (in minutes)

• Time (in days)

• mL (of tears)

Multiple Choice

Which answer represents an increasing interval?

• Pre-K to elementary

• Elementary to college

Function Maximums and Minimums

Maximum

A function's maximum is the point when its coordinate y is higher than higher than the ordinate of any other nearby points

Minimum

A function's minimum is the point where its coordinate y is lower than that of nearby points

It is possible to have both a maximum and a minimum on the same graph

Patient's Temperature

The graph shows a patient's temperature over 4 days.

The temperature was taken every 6 hours

Patient's Temperature

What was the maximum temperature and when did it occur?

What was the minimum temperature and when did it occur?

Fill in the Blanks

What was the maximum temperature and when did it occur?

Fill in the Blanks

What was the minimum temperature and when did it occur?

Multiple Select

Which answer(s) represent the increasing interval(s)?

• from 12:00 am on the first day until 12:00 pm on the second day

• from 12:00 pm on the second day until 12:00 on the fourth day

• from 12:00 am on the fourth day until 12:00 am on the fifth day

Car park

The graph shows the number of cars parked in a public car park in the city centre.

Fill in the Blanks

Over what period was the study carried out?

Fill in the Blanks

When did the number of cars reach a minimum? How many cars where there at that time?

Fill in the Blanks

When did the number of cars reach a maximum? How many cars where there at that time?