The amount of calories you consume after eating x pieces of candy is represented by the function y=150x. Find the domain of the function and determine whether it is discrete or continuous.

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The domain of a function is the input values of the function for which it exists.

Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:

y = 150x

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.

Learn more about discrete function here:

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The function is:

y = 150*x

where y is the number of calories consumed, and x is the number of pieces of candy consumed.

Now, the domain of a function is the possible values of x that you can input in the function.

For this particular case you can have:

x = 0 (no pieces candy)

x = 1 (one piece of candy)

x = 2 (two pieces of candy)

Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.

So we only use x = whole numbers.

Then the domain of the function is equal to all the natural numbers plus the zero, or:

D = {x ∈ N ∪ {0}}

"x belongs to the union between the set of the natural numbers and the zero"

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d is correct

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