Question

If graph of given function is shifted 6 units to the left, the new graph will represent the function ___________. If the graph of the given (first) function is shifted upwards by 6 units, the graph will represent the function ___________.

Choose answers for the first two blanks from these answers:

a. y = f(x + 6) = {x + 6)^
b. y = f(x - 6) = (x - 6)^
c. y = fx + 6 = x^ + 6
d, y = fx - 6 = x^ - 6

For the same y values. the

corresponding x values of the function y = f(x) = x

a. y = f 3x/2 = (3y/2)^
b. y = f 2x/3 = 2x/3^
c. y = fx + 1.5 = (x + 1.5)^
d. y = fx + 1.5 = x^ + 1.5

Answer 1

We know that if c is a positive real number, then the graph of f(x + c) is the graph of y = f(x) shifted to the left by c units.

Therefore, if the graph of given function y = f(x) is shifted 6 units to the left, the new graph will represent the function y = f(x+6).

Option a. is the correct answer.

If f(x) = x², then f(x+6) = (x+6)²

The 2^nd part has not been expressed clearly.

For the function y = f(x) = x², we have x = y^1/2 so that the inverse function is y = x^1/2 ( obtained by interchanging x and y).

For the function y = f(x) = (x+6)², we have x= y^1/2 -6 so that the inverse function is y = x^1/2 -6

Please make a comment about what is exactly required. The answer will then be suitably edited.

Also, please advise what is f(x).