Identify Applications of the Expression -8+3/(x+2): Rational Functions

Q: Why can't x equal -2 in this function?

When $ x = -2 $, the denominator becomes $ x + 2 = -2 + 2 = 0 $. Since division by zero is undefined, we must exclude this value from the domain.

Q: What happens to the -8 part when finding the domain?

The constant $ -8 $ doesn't affect the domain at all! It's a constant term that's always defined. Only the fractional part $ \frac{3}{x+2} $ can create restrictions.

Q: How do I write the domain properly?

You can write it as: all real numbers except -2, or in interval notation: $ (-\infty, -2) \cup (-2, \infty) $, or as $ x \neq -2 $.

Q: What if there were multiple fractions in the expression?

Find where each denominator equals zero separately, then exclude all those values from the domain. The domain is restricted by every fraction in the expression.

Q: Does the numerator 3 matter for the domain?

No! The numerator doesn't affect the domain. Even if it were 0, 100, or any other number, the domain restriction comes only from the denominator being zero.

Domain Determination with Rational Functions

Select the field of application of the following fraction:

$-8+\frac{3}{x+2}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the domain of substitution.

00:13 The domain exists to make sure we never divide by zero.

00:17 This means the denominator of our fraction must not be zero.

00:21 We'll use this rule for our exercise.

00:29 Let's isolate X to find the domain of substitution.

00:34 And there you have it! The domain of substitution is our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Select the field of application of the following fraction:

$-8+\frac{3}{x+2}$

Step-by-step solution

To solve this problem, we must find the domain of the expression $-8+\frac{3}{x+2}$ .

The domain of an expression is the set of all real numbers that don't cause any division by zero.

Let's analyze the expression:
We have $\frac{3}{x+2}$ as part of the expression. The critical part is the denominator $x+2$ .

Step 1: Set the denominator equal to zero to find the value that makes the fraction undefined:
$x + 2 = 0$

Step 2: Solve the equation for $x$ :
Subtract 2 from both sides:
$x = -2$

This shows that the fraction is undefined when $x = -2$ . Therefore, $-2$ must be excluded from the domain.

Conclusion: The domain of $-8+\frac{3}{x+2}$ is all real numbers except $-2$ .

Thus, the correct answer is: All numbers except (-2).

Final Answer

All numbers except (-2)

Key Points to Remember

Essential concepts to master this topic

Domain Rule: Rational functions exclude values making denominators zero
Technique: Set $x+2 = 0$ to find $x = -2$
Check: Verify $-8 + \frac{3}{-2+2} = -8 + \frac{3}{0}$ is undefined ✓

Common Mistakes

Avoid these frequent errors

Only focusing on the numerator instead of the denominator
Don't set the numerator equal to zero or ignore the denominator = wrong domain! The numerator being zero just makes the function equal zero, not undefined. Always find where the denominator equals zero to determine excluded values.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification shown below is correct:

$\frac{7}{7\cdot8}=8$

FAQ

Everything you need to know about this question

Why can't x equal -2 in this function?

When $x = -2$ , the denominator becomes $x + 2 = -2 + 2 = 0$ . Since division by zero is undefined, we must exclude this value from the domain.

What happens to the -8 part when finding the domain?

The constant $-8$ doesn't affect the domain at all! It's a constant term that's always defined. Only the fractional part $\frac{3}{x+2}$ can create restrictions.

How do I write the domain properly?

You can write it as: all real numbers except -2, or in interval notation: $(-\infty, -2) \cup (-2, \infty)$ , or as $x \neq -2$ .

What if there were multiple fractions in the expression?

Find where each denominator equals zero separately, then exclude all those values from the domain. The domain is restricted by every fraction in the expression.

Does the numerator 3 matter for the domain?

No! The numerator doesn't affect the domain. Even if it were 0, 100, or any other number, the domain restriction comes only from the denominator being zero.

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Identify Applications of the Expression -8+3/(x+2): Rational Functions

Domain Determination with Rational Functions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't x equal -2 in this function?

What happens to the -8 part when finding the domain?

How do I write the domain properly?

What if there were multiple fractions in the expression?

Does the numerator 3 matter for the domain?

🌟 Unlock Your Math Potential

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