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Algebra 1

4.3.2 Writing Statements from Function Notation

Algebra 14.3.2 Writing Statements from Function Notation

4.3.2 Writing Statements from Function Notation

4.3.2 • Writing Statements from Function Notation

Activity

The function P P gives the number of people, in millions, who own a smartphone, t t years after the year 2000. So, any value for which t t is negative would represent the number of years before 2000.

1. What does this equation tell us about smartphone ownership?

P ( 17 ) = 2320 P ( 17 ) = 2320

2. What does this equation tell us about smartphone ownership?

P ( − 10 ) = 0 P ( − 10 ) = 0

3. Use function notation to represent this statement.

In 2010, the number of people who owned a smartphone was 296,600,000.

4. Use function notation to represent this statement.

In 2015, about 1.86 billion people owned a smartphone.

5. Mai is curious about the value of t t in P ( t ) = 1000 P ( t ) = 1000 .

What would the value of t t tell Mai about the situation?

6. Mai is curious about the value of t t in P ( t ) = 1000 P ( t ) = 1000 .

Is 4 a possible value of t t here?

7. Use your own graph paper to sketch a graph of the function. Your graph should go through these four points: ( − 10 , 0 ) ( − 10 , 0 ) , ( 10 , 296.6 ) ( 10 , 296.6 ) , ( 15 , 1860 ) ( 15 , 1860 ) , and ( 17 , 2320 ) ( 17 , 2320 ) .

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Are you ready for more?

Extending Your Thinking

What can you say about the value or values of t t when P ( t ) = 1000 P ( t ) = 1000 ?

Video: Understanding Equations in Function Notation

Watch the following video to learn more about reading equations in function notation.

Understanding Equations in Function Notation

Self Check

The function Q gives the number of people, in millions, who owned a smart watch after 2015. What does the equation Q ( 6 ) = 7.25 mean?
  1. In 2021, 7.25 million more people owned smart watches than in 2015.
  2. In 2021, 7.25 million people owned smart watches.
  3. In the beginning of 2023, 6 million people owned smart watches.
  4. In 2006, 7.25 million people owned smart watches.

Additional Resources

Interpreting Equations in Function Notation

What does a statement like p ( 3 ) = 12 p ( 3 ) = 12 mean?

On its own, p ( 3 ) = 12 p ( 3 ) = 12 only tells us that when p p takes 3 as its input, its output is 12.

If we know what quantities the input and output represent, however, we can learn much more about the situation that the function represents.

If function p p gives the perimeter of a square whose side length is x x and both measurements are in inches, then we can interpret p ( 3 ) = 12 p ( 3 ) = 12 to mean “a square whose side length is 3 inches has a perimeter of 12 inches.”

We can also interpret statements like p ( x ) = 32 p ( x ) = 32 to mean “a square with side length x x has a perimeter of 32 inches,” which then allows us to reason that x x must be 8 inches and to write p ( 8 ) = 32 p ( 8 ) = 32 .

If function p p gives the number of blog subscribers, in thousands, x x months after a blogger started publishing online, then p ( 3 ) = 12 p ( 3 ) = 12 means “3 months after a blogger started publishing online, the blog has 12,000 subscribers.”

It is important to pay attention to the units of measurement when analyzing a function. Otherwise, we might mistake what is happening in the situation. If we miss that p ( x ) p ( x ) is measured in thousands, we might misinterpret p ( 36 ) p ( 36 ) to mean “there are 36 blog subscribers after x x months,” while it actually means “after 36 months, there are x x thousands of blog subscribers.”

Try it

Interpret Equations in Function Notation

If a function A A gives the area of a square, with a side length x x centimeters, then what does the function A ( 8 ) = 64 A ( 8 ) = 64 mean?

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