# Consider the following function: f(x) = \dfrac{x-1}{x^2 + 9x -10}. Determine if the following...

## Question:

Consider the following function: {eq}f(x) = \dfrac{x-1}{x^2 + 9x -10} {/eq}. Determine if the following statement is true or false: The function has no points of discontinuity.

## Discontinuity:

A function is discontinuous at a point if either of the three conditions is possible:

(1) The function is not defined at that point.

(2) The limit of the function does not exist at that point.

(3) The limit exists but the function is undefined.

In the case of a rational function, if the denominator becomes zero at a point, the function becomes undefined, and discontinuous as well. That point is known as the point of discontinuity.

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False.

The function is given as:

{eq}\begin{align} f(x) &= \dfrac{x-1}{x^2 + 9x - 10} \\[0.3cm] & = \dfrac{x-1}{x^2 + 10x - x - 10} \\[0.3cm]...