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The table shows the outputs y for different inputs x:


Input
(x) 3 7 11 15
Output
(y) 4 6 8 10


Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points)

Respuesta :

thisisbenmanley
Part A: Yes, the data represent a function. The definition of a function is a relation in which no value of x will have two different values of y.
(Every time you plug in 3 as x, you will always get 4 as y; it's ok if you plug in 3 and 5 as x and get the same y, you just can't get two different y's for one x; sorry, it is pretty confusing). None of the numbers in the table repeat, so we can safely say that the relation is a function.

Part B: All we have to do is plug in 11 for x in the function given to find the answer:
[tex]f(x)=5x-21\\f(x)=5(11)-21\\f(x)=55-21\\f(x)=34[/tex]
In the table, y = 8 when x = 11, but in the function given, y = 34 when x = 11, so the function given is greater.

Part C: To find the answer to C, just plug in 99 for f(x), as it tells you to do:
[tex]f(x) = 5x-21\\99=5x-21\\99+21=5x-21+21\\120=5x\\120/5=5x/5\\24=x[/tex]

Part A: Yes, because no input yields more than output values.

Part B: If f(x)= 5x-21, switch the x's to 11.

f(11)=5(11)- 21. 5 times 11 equals 55, then minus by 21. 55- 21= 34.

In the table, y=8 and x=11, but in the function, y=34 and x=11.

Part C:  I have to make sure to plug in 99 for f(x).

f(x)= 5x -21, which basically is 99= 5x -21.

Add 21 to both sides. 99+21 = 5x -21+21.

99 plus 21 =120, which 120= 5x.

Divide 120 by 5 and divide 5x by 5.

The answer will be 24

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