Given $b(x) = |x + 4|$, What Is $b(-10$\]?A. -10 B. -6 C. 6 D. 14

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Introduction to Absolute Value Functions

Absolute value functions are a fundamental concept in mathematics, particularly in algebra and calculus. They are used to represent the distance of a number from zero on the number line. In this article, we will explore the concept of absolute value functions and how to evaluate them.

What is an Absolute Value Function?

An absolute value function is a function that takes a real number as input and returns its absolute value as output. The absolute value of a number is its distance from zero on the number line. It is denoted by the symbol |x|, where x is the input number.

Evaluating Absolute Value Functions

To evaluate an absolute value function, we need to consider two cases: when the input number is positive and when it is negative.

  • If the input number is positive, the absolute value function returns the number itself.
  • If the input number is negative, the absolute value function returns the number with its sign changed.

Example: Evaluating the Absolute Value Function b(x) = |x + 4|

In this example, we are given the absolute value function b(x) = |x + 4|. We need to evaluate this function at x = -10.

Step 1: Substitute x = -10 into the function

b(-10) = |(-10) + 4|

Step 2: Simplify the expression

b(-10) = |-6|

Step 3: Evaluate the absolute value

Since the input number -6 is negative, the absolute value function returns the number with its sign changed.

b(-10) = 6

Conclusion

In this article, we have learned how to evaluate absolute value functions. We have seen how to substitute values into the function, simplify the expression, and evaluate the absolute value. We have also applied this knowledge to evaluate the absolute value function b(x) = |x + 4| at x = -10.

Answer

The correct answer is C. 6.

Additional Examples

Here are some additional examples of evaluating absolute value functions:

  • b(x) = |x - 3| at x = 5
  • b(x) = |2x + 1| at x = -2
  • b(x) = |x/2| at x = -4

Practice Problems

Try evaluating the following absolute value functions:

  • b(x) = |x + 2| at x = -3
  • b(x) = |3x - 1| at x = 2
  • b(x) = |x/3| at x = -6

Conclusion

In conclusion, absolute value functions are an important concept in mathematics. They are used to represent the distance of a number from zero on the number line. We have learned how to evaluate absolute value functions by substituting values into the function, simplifying the expression, and evaluating the absolute value. We have also applied this knowledge to evaluate the absolute value function b(x) = |x + 4| at x = -10.