Question
Question Suppose that \( g(x)=3 f(x) \) and that \( (-1,3) \) is a point on the graph of \( f(x) \). What are the coordinates of the poin on the graph of \( g(x) \) such that \( x=-1 \) ?
Ask by Lee Hanson. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The point on the graph of \( g(x) \) when \( x = -1 \) is \((-1, 9)\).
Solution
Given that \( g(x) = 3f(x) \), we need to find the coordinates of the point on the graph of \( g(x) \) when \( x = -1 \).
1. **Identify the Value of \( f(-1) \):**
- The point \( (-1, 3) \) is on the graph of \( f(x) \), which means \( f(-1) = 3 \).
2. **Calculate \( g(-1) \):**
\[
g(-1) = 3f(-1) = 3 \times 3 = 9
\]
3. **Determine the Coordinates:**
- The \( x \)-coordinate remains the same, \( x = -1 \).
- The \( y \)-coordinate is \( g(-1) = 9 \).
**Therefore, the coordinates of the point on the graph of \( g(x) \) when \( x = -1 \) are \((-1, 9)\).**
**Answer:** \((-1,\ 9)\)
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Simplify this solution Beyond the Answer
Since \( g(x) = 3 f(x) \) and we know the point \( (-1, 3) \) is on the graph of \( f(x) \), we can substitute \( x = -1 \) into the equation for \( g(x) \). First, we find \( f(-1) = 3 \). Now we can find \( g(-1) \): \[ g(-1) = 3 \cdot f(-1) = 3 \cdot 3 = 9. \] Thus, the coordinates of the point on the graph of \( g(x) \) when \( x = -1 \) are \( (-1, 9) \). In short, the point on the graph of \( g(x) \) is \( (-1, 9) \).
