Which function corresponds to the table?

The values of the variables in the table can be generated by a function, given that each input has exactly one output.

The function that corresponds to the table is C) y = -2·x + 3

Reasons:

To determine the type of function, the first difference between the y-values in the table are found as follows;

The difference between the consecutive y-values are;

1 - 3 = -2

-1 - 1 = -2

Therefore, the first difference is constant, therefore, the function is a linear function.

The equation of the function in point and slope form is therefore;

y - (-1) = -2·(x - 2)

y = -2·x + 4 - 1 = -2·x + 3

y = -2·x + 3

Therefore, the function that corresponds to the table is C) y = -2·x + 3

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Choice C) y = -2x+3



Work Shown:

Using the slope formula, find the slope of the line through (0,3) and (1,1)
m = (y2 - y1)/(x2 - x1)
m = (1 - 3)/(1 - 0)
m = (-2)/(1)
m = -2
The slope is -2

The y intercept is 3 since x = 0 leads to y = 3 in the first row of the table
So b = 3

Plug m = -2 and b = 3 into y = mx+b
y = mx+b
y = -2x+3

sin(angle) = opposite leg/ hypotenuse

sin(68) = 14/AC

AC = 14/sin(68)

Change to multiplication:

AC = 14 x cosec(68)

The answer is the second choice