Question: Select the graph of the function and its parent function.
g(x) = x - 4
Describe the transformation.
The graph of g is a translation ___ unit(s)
___ of the parent ___ function.
3
4
5
6
constant
linear
quadratic
absolute value
up
down
left
right
Graph shape position_hint: top-left. A linear parent function y = x is shown as a blue diagonal line through the origin, and the graph g is a red parallel diagonal line shifted 4 units down, representing g(x) = x - 4.
1. **State the problem:** We are given the function $$g(x) = x - 4$$ and asked to describe the transformation from its parent function.
2. **Identify the parent function:** The parent function is the linear function $$f(x) = x$$.
3. **Understand the transformation:** The function $$g(x) = x - 4$$ can be seen as the parent function $$f(x) = x$$ shifted vertically.
4. **Formula for vertical translation:** If $$g(x) = f(x) + k$$, then the graph of $$f(x)$$ is translated vertically by $$k$$ units.
5. **Apply to our function:** Here, $$g(x) = x - 4 = f(x) - 4$$, so $$k = -4$$.
6. **Interpret the sign of $$k$$:** Since $$k = -4$$, the graph is shifted 4 units down.
7. **Summary:** The graph of $$g$$ is a translation 4 units down of the parent linear function.
**Final answer:** The graph of $$g$$ is a translation 4 unit(s) down of the parent linear function.