Question

Which graph represents the following piecewise defined function?

Answer 1

I think I found the function and graphs in the choices. I chose Graph C that represents the given function.

g(x) = x² ; x < 0
g(x) = 1/2 x ; 0 < x < 4
g(x) = x ; x > 4

g(x) = -3² = 9    → (-3,9)
g(x) = 1/2 (4) = 2 → (4,2)
g(x) = 4 → (4,4) going to infinity

Answer 2

Option (C) is correct as the graph C represents functions.

Further explanation:

Domain is a set of all the possible values of the function. The value at which the function is defined is known as domain.

Range is a set of values that the function takes.

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

Explanation:

The functions are as follows,

(1) $g\left( x \right) = {x^2}$ for $x < 0$.

(2)$g\left( x \right) = \dfrac{1}{2}x$ for$0 < x \leqslant 4$

(3)$g\left( x \right) = x$ for $x > 4$

Substitute - 2 for x in function $g\left( x \right) = {x^2}$.

$\begin{aligned}g\left({ - 2}\right)&= {\left({ - 2}\right)^2}\\&=4\\\end{aligned}$

Substitute 4 for x in functiong $\left( x \right) = \dfrac{1}{2}x$

$\begin{aligned}g\left( 4 \right)&=\frac{1}{2}\left( 4 \right)\\&=2\\\end{aligned}$

Substitute 4 for x in function $g\left( x \right) = x.$

$g\left(4\right) = 4$

Option (A) is not correct as the graph A doesn’t represent the functions.

Option (B) is not correct as the graph A doesn’t represent the functions.

Option (C) is correct as the graph C represents functions.

Option (D) is not correct as the graph A doesn’t represent the functions.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Functions

Keywords:range, domain, codomain, relation, function, graph, coordinates, close interval, open interval, values.