Question

1. Jenny has a brand new home, and would like to be very adventurous in her decorating. She would like to put a series of murals on her walls. She has not decided how many murals she wants, or exactly how big she wants the murals to be. She does know that she wants the murals to be rectangular, and the length to be two feet more than the height. Write a function f(x) that gives the area of one of the rectangular murals, if the the height is x.

2.Jenny has a friend who paints murals to a homeowner's specifications, at a fee of $100 per mural plus an additional $40 per square foot of mural.
Write a function g(x) that gives the price of a mural that has an area of x square feet.

3.Jenny wants these two functions simplified down so that she can figure out the cost of the mural from just the height of the mural.
Find the cost of a mural of height x feet tall by finding g(f(x))

4.Jenny thinks that she might like murals of the same size in at least 4 rooms.
Find the cost of 4 murals of height x by finding 4*g(f(x))

5.Find the cost of one mural with a height of 6 feet.
Find the cost of 4 murals with a height of 4 feet.

6.Use a similar process to find the cost of 3 murals that have a height of 5 feet.

7.Jenny is getting worried about the cost of this project. She has realized that she probably needs to settle for two murals, and has decided that she wants to change the dimensions of her murals. She has decided the length should be twice the height. Write a function h(x) that gives the area of a mural with height x

Answer 1

Rectangular implies the area to be length times height

let height=x

let width=2 more than the height or Length=2+x

Area=F(x)=(2+x)(x)=2x+x^2

f(x)=x^2+2x

****************To Answer your Additional question

You see the standard price is $100 for any mural, And also charges $40 per square foot.

So to show you the approach, Lets say that a mural of 1 square feet needs to be painted, then the charge will be $100 plus the $40 for every square feet, then it will be 100+40(1 square feet)=$140.

The problem asks for the charge of mural whose area is x, so lets do the same thing.

$100+40(x square feet)=100+40x and that is the function that gives the price of mural with an area of x.

so, g(x)=100+40x