Question: Graph the given functions, $f$ and $g$, in the same rectangular coordinate system. Describe how the graph of $g$ is related to the graph of $f$. $f(x) = |x|$, $g(x) = |x| + 10$
1. **State the problem:** We are given two functions:
$$f(x) = |x|$$
$$g(x) = |x| + 10$$
We need to graph both on the same coordinate system and describe how $g$ relates to $f$.
2. **Recall the absolute value function:** The graph of $f(x) = |x|$ is a V-shaped graph with vertex at the origin $(0,0)$.
3. **Graph $f(x)$:** Plot points such as $(-2,2)$, $(0,0)$, $(2,2)$ to sketch the V shape.
4. **Graph $g(x)$:** Since $g(x) = |x| + 10$, this means we add 10 to every output of $f(x)$.
5. **Effect of adding 10:** Adding a constant outside the absolute value shifts the graph vertically.
6. **Plot points for $g(x)$:** For example, $g(-2) = 2 + 10 = 12$, $g(0) = 0 + 10 = 10$, $g(2) = 2 + 10 = 12$.
7. **Describe the transformation:** The graph of $g$ is the graph of $f$ shifted 10 units vertically up.
**Final answer:** The correct description is option A: The graph of $g$ is the graph of $f$ shifted 10 units vertically up.