Create an equation for the following graph:

- The graph has a y-intercept at -5.
- There are no x-intercepts.
- There are discontinuous points at (-1, -5) and (3, -5).

Given:

\[ y = \frac{(x+1)(x-3)}{(x+1)(x-3)} \]

This is incomplete. Can you provide guidance on how to finish the equation? Any help would be appreciated. Thank you.

that is close: you have the intercepts correct and the discontinuous point at x=-1 and x=3. The only thing is that you need to fix is the y values of the discontinuous points.
Without any coefficients, your graph is basically y=1, and you need it to resemble y=-5 to get the right y values. Normally, that just involves multiplication by -5 so multiply your function by -5 and you should get a correct graph.
And make sure to denote it with y= since it is an equation

Answered by paulcox | 2024-06-10

To create the equation for the given graph, use the rational function to maintain discontinuities at x = -1 and x = 3 while ensuring the y-intercept is at -5. The equation can be represented as y = − 5 ⋅ ( x + 1 ) ( x − 3 ) ( x + 1 ) ( x − 3 ) ​ , with x  = − 1 , 3 . This setup meets the requirement of no x-intercepts and correctly reflects the graph's characteristics.
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Answered by paulcox | 2024-12-16