Question

What are the new coordinates of the point (4,1/4) on the graph of the function f(x)=1/x after f(x) is vertically stretched by a factor of 8?

Answer 1

To find the new coordinates of the point \((4, \frac{1}{4})\) on the graph of the function \(f(x) = \frac{1}{x}\) after it is vertically stretched by a factor of 8, we follow these steps:

1. **Determine the original \(y\)-value**: We start with the point \((4, \frac{1}{4})\). Here, the \(x\)-coordinate is 4, and the corresponding \(y\)-coordinate is \(f(4) = \frac{1}{4}\).

2. **Apply the vertical stretch**: A vertical stretch by a factor of 8 means we multiply the \(y\)-value by 8. Therefore, the new \(y\)-value will be:
\[
y_{\text{new}} = 8 \cdot y_{\text{original}} = 8 \cdot \frac{1}{4} = 2.
\]

3. **Form the new coordinates**: The new coordinates after the vertical stretch will keep the same \(x\)-coordinate but have the updated \(y\)-coordinate. Thus, the new coordinates will be:
\[
(4, 2).
\]

In conclusion, the new coordinates of the point after the vertical stretch by a factor of 8 are \(\boxed{(4, 2)}\).