Question

a. the height of a mountain is a function of quality of the soil.
b. the potential energy is a function of height.
c. the number of weapons is a function of the number of people in that country.
d. the amount of rain is a function of number of clouds in sky.

1. identify the input and the output variables.

input variable = height
output variable = potential energy

1. write the function in the form \output is a function of the input.\ choose the correct answer below.

a. the potential energy is a function of height.
b. height is a function of potential energy.

1. explain how the example fits the definition of a function. choose the correct answer below.

a. for a given height, there is exactly one corresponding amount of potential energy.
b. for a given height, there can be more than one corresponding amount of potential energy.

Explanation:

Step1: Identify input - output for (i)

Given "The potential energy is a function of height", input is height and output is potential energy.

Step2: Write function for (ii)

As per the statement, the correct form is "The potential energy is a function of height", so option A is correct.

Step3: Explain function definition for (iii)

By the definition of a function, for a given input (height), there is exactly one output (potential energy). So option A is correct.

Answer:

i) Input variable: height, Output variable: potential energy
ii) A. The potential energy is a function of height
iii) A. For a given height, there is exactly one corresponding amount of potential energy