1) A: It is a function.
B) domain = {1, 2, 3, -2, -4}
C) range = {3, 0, -1, -3, -4}
2) A) Discrete function.
B) D: {0, 1, 2, 3, 4, 5, 6}
C) R: {$10, $8.50, $7, $5.50, $4, $2.50, $1}
How to know if this is a function?
A function is a relation that maps elements from the domain into elements from the range, such that each element from the domain can be mapped into only one element from the range.
In the diagram, we can see that each element on the domain (x) is being mapped into only one element of the range (y), so this is a function.
And by looking at the diagram we can see that:
- domain = {1, 2, 3, -2, -4}
- range = {3, 0, -1, -3, -4}
Now let's go to the second problem.
There is a gift card of $10, and we know that each song costs $1.50, then the credit left in the gift card as a function on the number of songs bougth is:
C (x)= $10 - $1.50*x
A) First, this function is discrete, because x can only take whole numbers.
B) The domain is the set of possible values that x can take.
The maximum value that x can take is such that the amoun left on the card is zero, so we solve:
$0 = $10 - $1.50*x
x = $10/$1.50 = 6.7
Rounding down to the nearest whole number:
x = 6
Then the domain (number of songs that can be bought with the gift card) is:
D: {0, 1, 2, 3, 4, 5, 6}
The range is the set of possible values taht C(x) can take, these are:
C(0) = $10
C(1) = $10 - $1.50 = $8.50
C(2) = $10 - $1.50*2 = $7
C(3) = $10 - $1.50*3 = $5.50
C(4) = $10 - $1.50*4 = $4
C(5) = $10 - $1.50*5 = $2.50
C(6) = $10 - $1.50*6 = $1
Then the range is:
R: {$10, $8.50, $7, $5.50, $4, $2.50, $1}
If you want to learn more about domain and range:
https://brainly.com/question/10197594
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