Question 1190840: 2. Determine whether each relation below is a function; then determine of it is invertible and explain your answer.
a) The relation that pairs the universal product code of an item at Target with its price.
b) The relation that pairs your height with the number of years you are old.
c) The relation that pairs the speed of your car in miles per hour with the speed in kilometers per hour.
Answer by math_tutor2020(3817)   (Show Source):
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Part (a)
x = universal product code
y = price
We have a function because each x value points to only one y value.
Any given code will have exactly one price. Assume that we focus on the final price if there is some kind of discount.
While we do have a function, we don't have an inverse.
This is because two products can share the same price.
If the price was the input, then it would produce more than one output. It wouldn't be clear what universal product code you wanted.
Eg: product 0001 is $4 and product 0002 is also $4
If someone said "I want a product that is $4", then it wouldn't be clear if they wanted product 0001 or product 0002
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Part (b)
x = height
y = age of the person
This relation is not a function.
For young people, they of course grow as they age.
Once reaching a certain age (it varies for everyone), the person will stop growing.
Let's say the person stops growing at age 20, and let's say they reach a height of 6 feet. This would mean the input x = 6 would pair with y = 20.
We would also have x = 6 pair with y = 21, and y = 22, and so on.
In other words, the input x = 6 produces multiple outputs. This shows we don't have a function.
The inverse is also not a function. It's possible that any input age can produce multiple height outputs. For example, not all 20 year olds are 6 feet tall.
Height and age are correlated but not directly connected.
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Part (c)
x = speed in mi per hour
y = speed in km per hour
When going from x to y, we have a function. This is because any given mph value has exactly one kph value.
We also have an inverse function as well because we can easily reverse the conversion going from kph back to mph again.
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