Given f(x)=|-5-4x|
, find the following: f(-4)


To find \( f(-4) \) given \( f(x) = |-5 - 4x| \):

1. Substitute \( x = -4 \) into the function:
   \[
   f(-4) = |-5 - 4(-4)|
   \]

2. Simplify inside the absolute value:
   \[
   = |-5 + 16|
   \]

3. Calculate the expression inside the absolute value:
   \[
   = |11|
   \]

4. Since the absolute value of 11 is 11:
   \[
   f(-4) = 11
   \]

So, \( f(-4) = 11 \).

Would you like further details or have any questions?

Here are some related questions to explore:

1. How would you find \( f(x) \) for any other \( x \)-value?
2. What is the range of \( f(x) = |-5 - 4x| \)?
3. How would the function change if it was \( f(x) = -5 - 4x \) instead of \( f(x) = |-5 - 4x| \)?
4. What is the vertex of the function \( f(x) = |-5 - 4x| \)?
5. How would you find \( f^{-1}(x) \) if \( f(x) = -5 - 4x \) (without the absolute value)?

**Tip:** When working with absolute values, simplify the expression inside the absolute value before applying the absolute function.

Given f(x) = |-5 - 4x|, find the following: f(-4)

Discover how to evaluate f(-4) for the function f(x) = |-5 - 4x|. This solution includes step-by-step simplification inside the absolute value, ideal for students learning basic algebra and absolute value properties. Suitable for Grades 8-10.

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