determine if the equation of the line f(x) = x + 1 a function using the Vertical Line Test?
To determine if the equation of a line, represented by f(x) = x + 1, is a function using the Vertical Line Test, we need to verify whether a vertical line passing through the graph would intersect the line at more than one point.
Here's how to perform the Vertical Line Test:
1. Imagine a vertical line and place it at different positions on the graph of the line f(x) = x + 1.
2. Move the line from left to right across the entire graph of f(x) = x + 1.
3. Observe whether the vertical line intersects the graph more than once for any x-values.
In the case of the equation f(x) = x + 1, no matter where you position the imaginary vertical line, it will only intersect the line at one point. Therefore, the equation passes the Vertical Line Test and is indeed a function.
Note that for every x-value you input into the equation f(x) = x + 1, you will always get a unique y-value, satisfying the definition of a function.