Sure! Let's go through each of the expressions provided to identify their corresponding parent functions.
1. [tex]\(x^3\)[/tex]:
- This is a cubic function. The parent function is simply [tex]\(y = x^3\)[/tex].
2. [tex]\(\sqrt{x}\)[/tex]:
- This is a square root function. The parent function is [tex]\(y = \sqrt{x}\)[/tex].
3. [tex]\(\frac{1}{x}\)[/tex]:
- This is a reciprocal function. The parent function is [tex]\(y = \frac{1}{x}\)[/tex].
4. [tex]\(x^2\)[/tex]:
- This is a quadratic function. The parent function is [tex]\(y = x^2\)[/tex].
5. [tex]\(2^x\)[/tex]:
- This is an exponential function where the base is 2. The parent function is [tex]\(y = 2^x\)[/tex].
6. [tex]\(|x|\)[/tex]:
- This is an absolute value function. The parent function is [tex]\(y = |x|\)[/tex].
By identifying these functions, we know that:
- [tex]\(x^3\)[/tex] corresponds to the parent function [tex]\(y = x^3\)[/tex]
- [tex]\(\sqrt{x}\)[/tex] corresponds to the parent function [tex]\(y = \sqrt{x}\)[/tex]
- [tex]\(\frac{1}{x}\)[/tex] corresponds to the parent function [tex]\(y = \frac{1}{x}\)[/tex]
- [tex]\(x^2\)[/tex] corresponds to the parent function [tex]\(y = x^2\)[/tex]
- [tex]\(2^x\)[/tex] corresponds to the parent function [tex]\(y = 2^x\)[/tex]
- [tex]\(|x|\)[/tex] corresponds to the parent function [tex]\(y = |x|\)[/tex]
These are the parent functions for the given expressions.
