Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Which of the following is the parent function of all absolute value functions?

A. [tex]f(x) = 3x[/tex]

B. [tex]f(x) = |x|[/tex]

C. [tex]f(x) = 2|x|[/tex]

D. [tex]f(x) = x^2[/tex]

Sagot :

GinnyAnswer
To determine the parent function of all absolute value functions, let's review the options provided:

1. [tex]\(f(x) = 3x\)[/tex]
2. [tex]\(f(x) = |x|\)[/tex]
3. [tex]\(f(x) = 2|x|\)[/tex]
4. [tex]\(f(x) = x^2\)[/tex]

### Step-by-Step Analysis:

1. Option [tex]\(f(x) = 3x\)[/tex]:
- This function represents a straight line with a slope of 3. It is a linear function but not an absolute value function.

2. Option [tex]\(f(x) = |x|\)[/tex]:
- This is the standard form of an absolute value function. Absolute value functions have a characteristic 'V' shape and can be written in the form [tex]\(f(x) = a|x - h| + k\)[/tex], where [tex]\(a\)[/tex], [tex]\(h\)[/tex], and [tex]\(k\)[/tex] are constants. The simplest or "parent" form of this function is [tex]\(f(x) = |x|\)[/tex].

3. Option [tex]\(f(x) = 2|x|\)[/tex]:
- This function is still an absolute value function but is scaled vertically by a factor of 2. Hence, it is a transformation of the parent function [tex]\(f(x) = |x|\)[/tex], not the parent function itself.

4. Option [tex]\(f(x) = x^2\)[/tex]:
- This function represents a parabola, which is a quadratic function. It is not an absolute value function.

Given these analyses, the parent function of all absolute value functions is:

[tex]\[f(x) = |x|\][/tex]

So, the correct answer is:
[tex]\[f(x) = |x|\][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.