Here's the word problem:
You have a coupon for $50 off your camera purchase of $100 or more at Camera World.
Write a function relating a camera's purchase price after coupon, y, to the retail price, x.
Give the domain of this function.
Here is what I have so far:
y = price after coupon x = original price
x - y >= 100 NOTE: >= is "greater than or equal to".
I don't think I wrote the function correctly. Also, I can't seem to remember what the "domain of a function" is.
Any help you could provide is very much appreciated.
y = x - 50
domain x>100
domain is the part of the x axis where the function is valid
for example the function
y = 1/x
domain is 0< x <0
but does not include x = 0
where it is undefined
To correctly write the function, consider the conditions for which the coupon is applied. In this case, the coupon is only valid for a purchase of $100 or more. So, the function relating the camera's purchase price after the coupon, y, to the retail price, x, can be defined as follows:
y = x - 50 if x >= 100
Here, if the original price x is greater than or equal to $100, the coupon of $50 is applied and subtracted from the original price to calculate the purchase price after the coupon. If the original price x is less than $100, the coupon cannot be applied, so y would be equal to x (no discount).
Now, let's talk about the domain of a function. In mathematics, the domain of a function refers to the set of values for which the function is defined or applicable. In this case, the domain would be all possible values of x, which are the retail prices of cameras.
Based on the word problem, we know that the coupon is applicable for purchases of $100 or more. Therefore, the domain of this function would be all real numbers greater than or equal to 100. In interval notation, we can express the domain as follows:
Domain: [100, +∞)
This indicates that x can be any value greater than or equal to 100.
In summary, the correctly written function relating the camera's purchase price after the coupon, y, to the retail price, x, is:
y = x - 50 if x >= 100
The domain of this function is [100, +∞), representing all values of x greater than or equal to 100.