Question

By considering the domains of the functions, match each function with its graph, labeled a) through d). $f(x)=\sqrt{x^{2}}$ a.Graph Can`t Copy b.Graph Can`t Copy c.Graph Can`t Copy d.Graph Can`t Copy

Name: Problem 96, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2021-01-26T04:35:48-08:00
Duration: 1 min 46 s
Channel: Carson Merrill
Description: By considering the domains of the functions, match each function with its graph, labeled a) through d). f(x)=√(x^2) a.Graph Can`t Copy b.Graph Can`t Copy c.Graph Can`t Copy d.Graph Can`t Copy

   By considering the domains of the functions, match each function with its graph, labeled a) through d).
$f(x)=\sqrt{x^{2}}$
a.Graph Can`t Copy
b.Graph Can`t Copy
c.Graph Can`t Copy
d.Graph Can`t Copy

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 96

Instant Answer

Solved by Expert Carson Merrill

01/26/2021

Step 1

The domain of the function $f(x) = \sqrt{x^2}$ is all real numbers, since any real number can be squared and then square rooted. Show more…

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By considering the domains of the functions, match each function with its graph, labeled a) through d). $f(x)=\sqrt{x^{2}}$ a.Graph Can`t Copy b.Graph Can`t Copy c.Graph Can`t Copy d.Graph Can`t Copy

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Key Concepts

Domain of a Function

This concept refers to the complete set of possible inputs (x-values) for which the function is properly defined. In functions involving square roots or denominators, determining the domain is essential to avoid undefined operations like taking the square root of a negative number or dividing by zero. Analysis of the domain helps in matching functions to their appropriate graphs.

Absolute Value Function

The absolute value function, denoted by |x|, outputs the non-negative magnitude of x. In the specific case of f(x)=?(x²), the expression simplifies to |x| because the square of x makes it non-negative and the square root returns the magnitude. This function is characterized by its V-shaped graph with a vertex at the origin, showing symmetry about the y-axis.

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