Question

Suppose g(x) = f(x – 2) + 3. Which statement best compares the graph of g(x) with the graph of f(x)?

Answer 1

Answer:

we conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units up.

Option A is correct

Step-by-step explanation:

To shift a function right

• Subtract inside the function's argument. For example, $f(x - b)$ is basically $f(x)$  shifted b units to the right.  

• Subtracting inside the function's argument moves you to the right.

So, g(x) = f(x – 2) means f(x) is shifted two units to the right.

and to move a function up

• Add outside the function. For example,  $f(x) + b$  is basically $f(x)$ moved up $b$ units.

So, g(x) = f(x – 2) + 3 means, f(x) is moved 3 units up.

Therefore, overall, after two transformations, we conclude

that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units up.

So, option A is correct.