Chapter 1: Q. 46 (page 121)

Use graphs to determine if each function is continuous at the given point x = c.
$f (x) = \{\begin{array}{ll} x^{2} - 3, if x rational \\ 3 x + 1, if x irrational, \end{array} c = 0$

Short Answer

Expert verified

The function is not continuous at x = 0.

Step by step solution

Step 1. Given information.

We have been given a function as:

$f (x) = \{\begin{array}{ll} x^{2} - 3, if x rational \\ 3 x + 1, if x irrational, \end{array} c = 0$

We have to determine if this function is continuous at the given point x = c.

Step 2. Draw the graph.

Step 3. Analyze the graph for the continuity of the function at x = c.

From the graph, we can see that:

For the rational values of x, $lim_{x \to 0} f (x) = - 3$

For the irrational values of x, $lim_{x \to 0} f (x) = 1$

These two values are different.

Therefore, this function is not continuous at x = 0.

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Use graphs to determine if each function is continuous at the given point x = c.
$f (x) = \{\begin{array}{ll} x^{2} - 3, if x rational \\ 3 x + 1, if x irrational, \end{array} c = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Draw the graph.

Step 3. Analyze the graph for the continuity of the function at x = c.

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Use graphs to determine if each function is continuous at the given point x = c.f(x)=x2−3, ifxrational3x+1, ifxirrational,c=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Draw the graph.

Step 3. Analyze the graph for the continuity of the function at x = c.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Applied Mathematics

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use graphs to determine if each function is continuous at the given point x = c.
$f (x) = \{\begin{array}{ll} x^{2} - 3, if x rational \\ 3 x + 1, if x irrational, \end{array} c = 0$