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MA.912.A.2.3 Functions

What You Need To Know...

Functions, function notation, determine whether a given relation is a function, and link equations to functions.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. Items may use a variety of forms, including graphs, tables, sets of points, or equations.
  3. Items may ask to determine the equation of a function.
  4. Items may use function notation.  

Example One

Andrew plotted a set of points on the coordinate grid shown below.  All of the points have integer coefficients.

 A2_Sample_2.png

 

Which of the following points could be removed so that Andrew's graph represents a function?

  1. (-4, -3)
  2. (-2, 1)
  3. (0, 0)
  4. (2, -2)

CLICK HERE FOR SOLUTION

Example Two

The function shown below is used to convert a temperature, x, in degrees Fahrenheit (°F), to a temperature, f(x), in degrees
Celsius (°C).

 a23_sample_2_eq.png

Micah wanted to convert today's high temperature of 77°F to °C.  What is today's high temperature in °C?

blank_grid.png

 

CLICK HERE FOR SOLUTION

Example Three

For one child, a childcare facility charges $300 per month for preschool and $3.50 per hour for each hour of childcare after preschool.  The function below can be used to determine f(h), the monthly fee for childcare and preschool, where h represents the number of hours spent in childcare after preschool.

f(h) = 300 + 3.5h

If the one-month charges for one child totaled $637.75, what was the total number of hours the child spent in childcare after preschool?

Answer grid.jpg

 

 

CLICK HERE FOR SOLUTION

Example Four

As a diver swims deeper underwater, the water pressure in pounds per square inch (PSI) increases on the diver.  The table below shows the pressure in PSI for several depths of water.

WATER PRESSURE

Depth (in feet)  Pressure (in PSI)
 10  4.3
 20  8.6
 30  12.9
 40  17.2
 50  21.5


Which equation represents p, the water pressure in square inches, as a function of d, the depth in feet?

A.  p =   4.3d
B.  p =   0.43d
C.  p = 23.3d
D.  p =   2.33d

 

CLICK HERE FOR SOLUTION

Additional Examples

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Function Notation

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Relations & Functions

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Vertical Line Test

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Equations from Functions

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Reference Sheet