The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function? a)
(1, 9) b) (8, 9) C) (−3, 3) d) (−6, −5)

Options a,b and c preserves the function

Step-by-step explanation:

Assuming the missing table is the one shown in the attachment

we know that

A function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output

In this problem

If the point (-6,-5) is added, the function is not preserved, because for one input it will have two outputs

so

For x=-6

y=9 and y=-5

If the other points are added the function is preserved, because for one input it will have one output

therefore

Options a,b and c preserves the function

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!