Explore

 

In Try This 1 you explored how some values related to GST can be determined. For some of the values, you added or subtracted previously calculated values.

 

For example, to determine the difference in the amount of tax, you may have

• 

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  determined the amount of tax at 7% (0.07x)
• determined the amount of tax at 5% (0.05x)
• subtracted the two amounts (0.07x − 0.05x = 0.02x)

It is possible to use function notation to describe this process. Let

• x be the amount purchased
• f(x) be the amount of tax paid at 7%
• g(x) be the amount of tax paid at 5%
• h(x) represent the difference between the two amounts

You can then write h(x) = f(x) − g(x), which is sometimes written as h(x) = (f − g)(x). In this scenario,

 

 

The advantage to writing the difference of the two functions as one function in function notation is that it allows you to make more general statements. For example, you can define p(x) and q(x) as the amounts of tax paid on a purchase of x dollars, and then define r(x) as the difference. This means you can write r(x) = p(x) − q(x) without even knowing how p(x) and q(x) can be determined!

 

Just as you could subtract two functions, it is also possible to add two functions. You could write the sum of the two functions as h(x) = f(x) + g(x), which can also be written h(x) = (f + g)(x).

 

In Try This 2 you will explore how specific functions can be added.

 

Try This 2

 

Consider the functions f(x) = x2 + x and g(x) = 3x − 1.

1. Use the functions noted to complete the following table.
   
   

   x	f(x)	g(x)
   −5
   −2
   0
   2
   5

2.  
   1. Substitute f(x) = x2 + x and g(x) = 3x − 1 into h(x) = f(x) + g(x).
   2. Use the resulting expression to determine h(x) when x = −5, −2, 0, 2, and 5.
   3. Substitute f(x) = x2 + x and g(x) = 3x − 1 into p(x) = f(x) − g(x).
   4. Use the resulting expression to determine p(x) when x = −5, −2, 0, 2, and 5.
   5. How did the values you determined in questions b. and d. relate to the values you determined in the table in question 1?
   6. Suggest a general rule for adding or subtracting functions that are written as equations.

Save your responses in your course folder.