The function g(x) = x2 is transformed to obtain function h:

Question

h(x) = g(x) + 1.

Which statement describes how the graph of h is different from the graph of g?

A.
The graph of h is the graph of g vertically shifted down 1 unit.
B.
The graph of h is the graph of g horizontally shifted right 1 unit.
C.
The graph of h is the graph of g vertically shifted up 1 unit.
D.
The graph of h is the graph of g horizontally shifted left 1 unit.

Answer 1

The graph of the function \( g(x) = x^2 \) is a parabola that opens upwards with its vertex at the origin (0, 0). The function \( h(x) = g(x) + 1 \) can be rewritten as \( h(x) = x^2 + 1 \).

Adding 1 to the function \( g(x) \) shifts the entire graph of \( g \) upwards by 1 unit. Therefore, the vertex of the parabola shifts from (0, 0) to (0, 1).

Based on this information, the correct statement that describes how the graph of \( h \) is different from the graph of \( g \) is:

C. The graph of h is the graph of g vertically shifted up 1 unit.