1. ## [SOLVED] Confusing Functions

I've tried to do the following questions with the help of provided examples but can't seem to get a right answer. I don't think I am solving them with the right method.

1) A piece of wire $\displaystyle 24 cm$ long has the shape of a rectangle. Given that the width is $\displaystyle w cm$, show that the area, $\displaystyle A cm^2$, of the rectangle is given by the function $\displaystyle A = 36-(6-w)^2$. Find the greatest possible domain and the corresponding range of this function in this context.

2) Sketch the graph of $\displaystyle y = x(8-2x)(22-2x)$

Given that $\displaystyle y cm^3$ is the volume of a cuboid with height $\displaystyle x cm$, length $\displaystyle (22-2x) cm$ and $\displaystyle width (8-2x) cm$, state an appropriate domain for the function given above.

Can you also please tell me how would I go on about sketching these kind of graphs.

2. Originally Posted by unstopabl3
I've tried to do the following questions with the help of provided examples but can't seem to get a right answer. I don't think I am solving them with the right method.

1) A piece of wire $\displaystyle 24 cm$ long has the shape of a rectangle. Given that the width is $\displaystyle w cm$, show that the area, $\displaystyle A cm^2$, of the rectangle is given by the function $\displaystyle A = 36-(6-w)^2$. Find the greatest possible domain and the corresponding range of this function in this context.

2) Sketch the graph of $\displaystyle y = x(8-2x)(22-2x)$

Given that $\displaystyle y cm^3$ is the volume of a cuboid with height $\displaystyle x cm$, length $\displaystyle (22-2x) cm$ and $\displaystyle width (8-2x) cm$, state an appropriate domain for the function given above.

Can you also please tell me how would I go on about sketching these kind of graphs.

HI

(1) The width is w , then let the other side be x .

2x+2w=24 .... x+w=12

A=wx

A=w(12-w)

A=12w-w^2

A-36=12w-w^2-36

A-36=-(36-12w+w^2)

A-36=-(6-w)^2

A=36-(6-w)^2

When you graph this , it has an 'n' shape so w=6 and the correspoinding range would be 36 .