Question

Write a formula for the function obtained when the graph of f(x)=|x| is shifted down 3 units and to the right 1 unit.(1 point)
Responses

g(x)=|x−1|−3
g(x)=start absolute value x minus 1 end absolute value minus 3

g(x)=|x+1|+3
g(x)=start absolute value x plus 1 end absolute value plus 3

g(x)=|x+3|−1
g(x)=start absolute value x plus 3 end absolute value minus 1

g(x)=|x+1|−3

Answer 1

To shift the function \( f(x) = |x| \) down 3 units and to the right 1 unit, we need to adjust the formula accordingly.

1. **Shifting down 3 units** means we subtract 3 from the entire function: \( |x| - 3 \).
2. **Shifting to the right 1 unit** means we replace \( x \) with \( x - 1 \): \( |x - 1| \).

Combining both transformations, we have:
\[
g(x) = |x - 1| - 3
\]

So, the correct formula is:
\[
g(x) = |x - 1| - 3
\]

This corresponds to the first option:
**g(x)=|x−1|−3**.