Question

The graph of f, of, x, equals, minus, vertical bar, x, vertical barf(x)=−∣x∣ is given below. Write the equation of a function g, of, xg(x) which would shift the graph of f, of, xf(x) left 4 units and up 2 units.

Answer 1

To shift the graph of the function \( f(x) = -|x| \) left 4 units and up 2 units, we need to apply transformations to the function.

1. **Shift Left 4 Units**: To shift a function left, we replace \( x \) with \( x + 4 \). So, the function \( f(x) \) becomes:
\[
f(x + 4) = -|x + 4|
\]

2. **Shift Up 2 Units**: To shift a function up, we add 2 to the entire function. Therefore, we take the result from the first step and add 2:
\[
g(x) = -|x + 4| + 2
\]

Combining both transformations, the function \( g(x) \) that represents the new graph after the shifts is:
\[
g(x) = -|x + 4| + 2
\]