Question

Which statement is correct regarding and the parent function ?

The domains of g(x) and f(x) are the same, but their ranges are not the same.
The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
The missing parts of the question are in the picture

Answer 1

C

Explanation:

just did it on edge

Answer 2

Original Function:


`\sf\sqrt[\sf 3]{\sf x}`

If you add something inside the square root, it will shift the graph of the function to the left that same amount of units.

Example:
`\sf\sqrt[\sf 3]{\sf x+4}`

Shifts the original function to the left 4 units.

If you subtract something inside the square root, it will shift the graph of the function to the right that same amount of units.

Example:
`\sf\sqrt[\sf 3]{\sf x-6}`

Shifts the original function to the right 6 units.

If you add something outside of the square root, it will shift the graph of the function up that same amount of units.

Example:
`\sf\sqrt[\sf 3]{\sf x}+3`

Shifts the original function up 3 units.

If you subtract something outside of the square root, it will shift the graph of the function down that same amount of units.

Example:
`\sf\sqrt[\sf 3]{\sf x}-2`

Shifts the original function down 2 units.

So in the case of
`\sf\sqrt[\sf 3]{\sf x+6}-8`, it will shift the original function 6 units to the left and 8 units down.

The domain is the x-values. The x-values of the original function is all real numbers. Shifting the graph down and to the left would not change the domain.

The range is the y-values. The y-values of the original function is all real numbers. Shifting the graph down and to the left would not change the domain.

So your answer is C.