Answer to Question #125873 in Algebra for Mandisa Mnguni

Question

The income tax a person pays depends on the person's total income.
The number of years of experience on a job has a direct bearing on the salary recieved.
The amount by which your savings will grow in a year depends on the interest offered by the bank.
The area of a circle depends on the raduis of the circle.
The distance traveled in a car at a certain rate depends on the time travelled.

a) Express each situation in functional words. For ecample, the income tax is a function of the total income.
b) For each situation, indicate the dependent and independent variable.
c) write the two variables as an ordered pair, and write the function using the notation y=(x)
d) Explain the meaning of a function in your own words, Illustrate with your own specific example.

Answer 1

a) Income tax is a function of the total income

Number of years of experience is a function of the salary received

The interest rate of the bank is a function of the total amount of savings

The radius of a circle is a function of the area.

The distance traveled is a function of the time traveled at a constant speed.

b) Income tax is the independent variable Total Income is the dependent variable

Salary received is the dependent variable while Number of years is the independent variable.

Interest rate of the bank is the independent variable while the total amount of savings is the dependent variable.

Radius of the circle is the independent variable while the area is the dependent variable.

The distance traveled is the dependent variable while the time traveled is the independent variable.

c) Total income = f(Income Tax)

Salary Received = f(Number of experienced years)

Total Amount of Savings = f(Interest rate of the bank)

Area = f(Radius)

Distance = f(Time)

d) A function in algebra is an equation that allows for the entry of a domain or a value that represents a figure or fact and be able to evaluate it mathematically to get the desired output which can be referred to as the range. An example is f(x) = y² +4. The value of x changes every time the value of y is altered. This shows that a function has both independent and dependent variable.