Which of the following correctly analyzes the effect on the graph of the function

f(x) = 1/x when it is replaced by g (x) = 1/x+21? (1 point)
A. The graph of f (x) is shifted right 21 units.
B. The graph of f (x) is shifted left 21 units.
C. The graph of ƒ (x) is shifted up 21 units.
D. The graph of ƒ (a) is shifted down 21 units.

1 answer

To analyze the effect of the transformation from \( f(x) = \frac{1}{x} \) to \( g(x) = \frac{1}{x} + 21 \), we need to consider how the function \( g(x) \) changes the graph of \( f(x) \).

In the function \( g(x) = \frac{1}{x} + 21 \), the \( +21 \) indicates a vertical shift of the graph of \( f(x) \). Specifically, adding 21 to the function \( f(x) \) lifts every point on the graph of \( f(x) \) up by 21 units.

Therefore, the correct analysis of the effect on the graph is:

C. The graph of \( f(x) \) is shifted up 21 units.