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I need some help on this ASAP please. Thanks!


The table shows the outputs y for different inputs x:


Input

(x)

5 6 7 8


Output

(y)

2 5 8 11


Part A: Do the data in this table represent a function? Justify your answer.

Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7?

Part C: Using the relation in Part B, what is the value of x if f(x) = 75?

Verified Answer :

texaschic101
Ayes...it is a function because there is no repeating x values.
B. (5,2)(6,5)...slope = (5 - 2) / (6 - 5) = 3
y = mx + b
slope(m) = 3
(5,2)...x = 5 and y = 2
now we sub
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
so the equation is : y = 3x - 13
when x = 7
y = 3(7) - 13....y = 21 - 13....y = 8

f(x) = 2x + 13...when x = 7
f(7) = 2(7) + 13...f(7) = 14 + 13.....f(7) = 27

the function has a greater value

C. f(x) = 2x + 13....when f(x) = 75
75 = 2x + 13
75 - 13 = 2x
62 = 2x
62/2 = x
31 = x

ankitprmr2

Part A: In the given problem we have given values of x and values of y.

Part B: f(x) = 2x + 13 has greater value at x= 7

Part C: The value of x is 31.

One key point to observe is that for each x there is a unique y hence the given data belongs to a function but the equation of this function is not known.

Let us fit a line into the given data of x and y which can be given by the formula:

\({y-y_1} = ((y_2-y_1)}/{(x_2-x_1)}) \times (x-x_1})\)   ....(1)

Putting the values from data in equation (1)

we get y-2= ((5-2)/(6-5)) (x-5)

(Taking first two points for instance)

y-2 = 3( x- 5) y= 3x-13     ....(2)

Part B : Another function is given in the question is

f(x) = 2x +13 ....(3)

Now, we can find out the values of equation (2) and equation (3) for x= 7.

Putting in equation (2) we can get y(7) = 21-13 = 8.

Similarly,

f(7) = 2 \(\times\) 7 + 13 f(7) = 14 +13 = 27

so we can conclude that equation (3) has a greater value at x =7.

Part C :

Using the relation that is concluded in Part B

75 = 2x +13

75-13= 2x

62 = 2x

x = 31

Thus, the value of x is 31.

For more information please refer to the link below:

https://brainly.com/question/7639434

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