Question

The equation is attached and the questions are based on the equation attached Questions 1)The function f(x) is shifted horizontally...?A) 2 units to the left of g(x)B)2 units to the right of g(x)C) The function is not shifted horizontally from g(x)2) The function f(x) is shifted vertically...? A) 3 units up from g(x)B) 3 units down from g(x)C) The function is not shifted vertically from g(x)

Answer 1

When a function is shifted horizontally, then they have the next form:

f(x+c), the function f(x) has an horizontal translation left c units.

f(x-c), the function f(x) has an horizontal translation right c units.

When a function is shifted vertically, they have the next form:

f(x) + d, the function f(x) has a vertical translation up d units.

f(x) - d, the function f(x) has a vertical translation down d units.

Let find f(x):

We have that f(x)= g(x) + 3

Where g(x)=(x-2)²

Replacing:

f(x)=(x-2)² + 3

Then, the function is translated horizontal 2 units to the right and it is vertical shifted 3 units up.

Hence, the answers are:

1) The answer is "B)2 units to the right of g(x)"

2) A) 3 units up from g(x)