Question

The function f(x) = x² is transformed to create the function g(x) = f(x) + 5. What statement is true comparing f(x) and g(x)?

g(x) is shifted 5 units to the LEFT,
g(x) is shifted 5 units to the RIGHT,
g(x) is shifted 5 units UP,
g(x) is shifted 5 units DOWN,

Answer 1

The function g(x) = f(x) + 5 is created by shifting the function f(x) = x² 5 units up.

Step-by-step explanation:

The function g(x) = f(x) + 5 is created by transforming the function f(x) = x². To understand the transformation, we can compare f(x) and g(x):

• f(x) = x² is a parabola that opens upwards with its vertex at the origin (0, 0).
• Adding 5 to f(x) moves the entire graph of f(x) vertically 5 units up.
• Therefore, g(x) = f(x) + 5 is a parabola that opens upwards with its vertex at (0, 5).

So, the statement that is true comparing f(x) and g(x) is: g(x) is shifted 5 units UP.