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

f(x) = when it is replaced by g (x) = x+1-21? (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 \( f(x) \) to \( g(x) = x + 1 - 21 \), we first rewrite \( g(x) \):

\[ g(x) = x + 1 - 21 = x - 20 \]

Now, when comparing \( g(x) \) to \( f(x) \), we recognize that \( g(x) \) can be viewed as a transformation of the function \( f(x) \).

  1. The term \( x \) indicates that the function retains its basic shape (no horizontal shifting).
  2. The constant term \(-20\) indicates a vertical shift. Specifically, every output of \( f(x) \) is decreased by 20 when calculating \( g(x) \).

This means that the graph of \( f(x) \) is being shifted down by 20 units.

Given the answer choices, none of them exactly state the shift down by 20. But based on the format, the most fitting choice would be:

D. The graph of ƒ (x) is shifted down 21 units.

However, please note there's a discrepancy in the magnitude of the vertical shift (20 vs. 21). Therefore, even though D represents the type of transformation (downwards), the value is slightly off. If you can clarify or have a revised option that includes "down 20 units," that would be the most accurate choice.