# 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.

## Answer and Explanation: 1

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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]...

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Chapter 1 / Lesson 9What is a discontinuous function? Explore discontinuous function examples and learn when is a function discontinuous and how to find discontinuity of a function.

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