Question

The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x). Write your answer in the form a|x–h|+k, where a, h, and k are integers or simplified fractions. went down 1

Answer 1

To translate the function \( f(x) = |x| \) to create the function \( g(x) \), we need to consider both vertical and horizontal translations. Given that the function \( g(x) \) is a translation of \( f(x) \) that "went down 1", we can analyze this as a vertical shift.

1. The original function \( f(x) = |x| \) has its vertex at the origin (0, 0).
2. The vertical shift "down 1" means we subtract 1 from \( f(x) \).

So, the function \( g(x) \) will be:
\[
g(x) = |x| - 1
\]

To express this in the required form \( g(x) = a|x-h| + k\):
- In this case, \( a = 1 \) (the coefficient of the absolute value),
- \( h = 0 \) (there is no horizontal shift),
- \( k = -1 \) (the vertical shift down).

Therefore, the function rule for \( g(x) \) in the specified form is:
\[
g(x) = 1 |x - 0| - 1
\]
or simply:
\[
g(x) = |x| - 1
\]

Thus, the values of \( a\), \( h\), and \( k\) are:
\[
a = 1, \quad h = 0, \quad k = -1
\]