If a function is symmetry over the line x=2, what kind of function could it be ? a . absolute value b. cubic c . exponential d . rational

 The answer is (A) Absolute value.

Step-by-step explanation:  Given that we have a function which is symmetric over the line x = 2.

Obviously, the graph of the line x = 2 will be vertical, parallel to Y-axis.

But, the graphs of a cubic function, exponential function and a rational function will not be always parallel to the Y-axis. So, these three options will not work here.

The only correct choice is the absolute function.

For example, for the given line x = 2, the function which is symmetric to it will be of the form

where 'k' is any real number.

The attached figure is drawn for k=2.

Thus, the correct option is (A). Absolute value.

answer: c

substitute in the values.

for a:

f(0) = 0 + 9

f(0) = 9

a is a solution.

for b:

f(7) = 14 + 9

f(7) = 23

b is a solution.

for c:

f (3) = 6 + 9

f(3) = 15

c is not a solution. it's supposed to be 14.

for d:

f(2) = 4 + 9

f(2)= 13

d is a solution.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal