Question

Analyze the effect on the graph of f(x)=1x when it is replaced by g(x)=1x−12 . Option #1: It shifts up 2 units. Option #2: It shifts down 12 unit. Option #3: It shifts up 12 unit. Option #4: It remains unaffected. (1 point)

Answer 1

To analyze the effect of the transformation from \( f(x) = \frac{1}{x} \) to \( g(x) = \frac{1}{x} - 12 \), we need to consider how the graph of \( f(x) \) is altered by the function \( g(x) \).

1. \( f(x) = \frac{1}{x} \) is the original function.
2. In \( g(x) = \frac{1}{x} - 12 \), we see that the term \(-12\) has been added to the function.

This represents a vertical shift of the graph. Specifically, subtracting a value from a function will shift the entire graph downward by that value. Since we have \(-12\) added to the original function, the graph of \( g(x) \) shifts down by 12 units.

Thus, the correct option is:

**Option #2: It shifts down 12 units.**