Answered

IDNLearn.com is your go-to resource for finding answers to any question you have. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.

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 :

GinnyAnsweridn
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 contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.