a. the height of a mountain is a function of quality of the soil.\nb. the potential energy is a function of…

a. the height of a mountain is a function of quality of the soil.\nb. the potential energy is a function of height.\nc. the number of weapons is a function of the number of people in that country.\nd. the amount of rain is a function of number of clouds in sky.\n1) identify the input and the output variables.\ninput variable = height\noutput variable = potential energy\n2) write the function in the form \output is a function of the input.\ choose the correct answer below.\na. the potential energy is a function of height.\nb. height is a function of potential energy.\n3) explain how the example fits the definition of a function. choose the correct answer below.\na. for a given height, there is exactly one corresponding amount of potential energy.\nb. for a given height, there can be more than one corresponding amount of potential energy.

a. the height of a mountain is a function of quality of the soil.\nb. the potential energy is a function of height.\nc. the number of weapons is a function of the number of people in that country.\nd. the amount of rain is a function of number of clouds in sky.\n1) identify the input and the output variables.\ninput variable = height\noutput variable = potential energy\n2) write the function in the form \output is a function of the input.\ choose the correct answer below.\na. the potential energy is a function of height.\nb. height is a function of potential energy.\n3) explain how the example fits the definition of a function. choose the correct answer below.\na. for a given height, there is exactly one corresponding amount of potential energy.\nb. for a given height, there can be more than one corresponding amount of potential energy.

Answer

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