Question
Which functions shows the function \( f(x)=3^{x} \) being translated 5 units down? \( f(x)=3^{x-5} \) \( f(x)=3^{x}+5 \) \( f(x)=3^{x+5} \) \( f(x)=3^{x}-5 \)
Ask by Ellis Mcguire. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(x) = 3^{x} - 5 \)
Solution
To translate the function \( f(x) = 3^{x} \) **5 units down**, you subtract 5 from the original function. This modifies the function as follows:
\[
f(x) - 5 = 3^{x} - 5
\]
So, the correct translated function is:
\[
f(x) = 3^{x} - 5
\]
**Answer:**
\( f(x) = 3^{x} -5 \)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To translate the function \( f(x) = 3^x \) down by 5 units, you would subtract 5 from the function. This results in the equation \( f(x) = 3^x - 5 \). So, the correct answer is \( f(x) = 3^x - 5 \). When translating functions vertically, remember that subtracting a value moves the graph downward, while adding it moves it up! So if you ever want to go up or down the vertical graph, just play around with the plus or minus signs!
