Question

Consider the following examples in real-world situations that describe a correspondence between phenomena:

(a) Express each situation in functional words. For example, the income tax is a function of the total income. (8)

(b) For each situation, indicate the dependent and independent variable. (5)

(c) Write the two variables as an ordered pair, and write the function using the notation

Answer 1

$$Solution$$

a.) To answer the question, Let's take the income tax T owed in a certain state to be a function of the total income I both measured in dollars. The formula will be

$$T = 0.11 I - 500:$$

Words:

• To find the income tax, multiply the total income by 0.11 then subtract 500 from the value
• To find the total income, add the income tax to 500 and divide the value by 0.11

b.) We have a relationship between T and I such that each value of I determines exactly one value of T. In this case, since T depends on I, It makes sense to call I the independent Variable and T the dependent variable

c.) Two variables as an ordered pair is $(I,T).$ Next,$f(I,T)=Z$

$\implies f(I,T)=0.11I-T-500$