Question
\( \leftarrow \quad \) Write the function whose graph is the graph of \( y=\sqrt{x} \), but is shifted down 5 units.
Ask by Matthews Weston. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The function shifted down 5 units is \( y = \sqrt{x} - 5 \).
Solution
To find the function whose graph is the graph of \( y = \sqrt{x} \) shifted down 5 units, we need to subtract 5 from the original function.
1. Start with the original function:
\[
y = \sqrt{x}
\]
2. To shift the graph down by 5 units, we subtract 5 from the function:
\[
y = \sqrt{x} - 5
\]
Thus, the function whose graph is the graph of \( y = \sqrt{x} \) shifted down 5 units is:
\[
y = \sqrt{x} - 5
\]
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Simplify this solution Bonus Knowledge
To derive the function for the graph of \( y = \sqrt{x} \) shifted down 5 units, you just need to subtract 5 from the original function. Thus, the new function becomes: \[ y = \sqrt{x} - 5 \] This new equation will produce a graph that retains the same shape as the original square root function, but every point on the graph will be moved down 5 units along the y-axis. So if you had any points on \( y = \sqrt{x} \), for example \( (1, 1) \), they would now appear at \( (1, -4) \) on the new graph. Happy graphing!
