A small skateboard company is trying to determine the best price for its boards. When the boards are priced at 80 dollars, 120 are sold. The company finds that each increase of 5 dollars will result in selling 15 fewer boards.
1) Solve the domain and range 2) Determine the inverse and what it represents
I got $R=(80+5x)(120-15x)$
Now as for the domain and range. I think I would need to solve for x, find the positive number and that would be my max domain. For the range I would need to find the max height (money) and would that be my max range?
I have no clue how to find the inverse though. I would assume I would need to convert to quadratic form and then complete the square?
I'm in grade 11 math.
For future reference, try and demonstrate your efforts when asking a question.
When the price is $80$ come in we have f(80)=120. Then f(80+5x)=120-15x. So, we can take a stab at our function now and say notice this function changes linearly. So, we just need two points to get an equation of a line and we were given (80,120) start. Now, choose $x=1$ and so f(85)=105. So $(85,105)$. So the slope of our line is
$$\frac{105-120}{85-80}=-3$$
and it doesn't take much work to figure out that $x=8$ we get $f(120)=0$. And so in point slope form
$$f(x)=-3x-120$$
There are of course several other ways to have figured this out. Applying the logical restrictions of the equation (you can't sell negative skateboards for example) should help you figure the rest out.