Respuesta :
It would be a parabola that opens up. It will have the oirgin of (0,0) Here are some of the points of the graph:
(-2,2)
(-1,.5)
(0,0)
(1,.5)
(2,2)
Hope this helps :)
(-2,2)
(-1,.5)
(0,0)
(1,.5)
(2,2)
Hope this helps :)
For the graph of function [tex]f\left( x \right)=\dfrac{1}{2}{x^2}[/tex], kindly refer to the image attached.
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 is as follows,
[tex]f\left( x \right)=\dfrac{1}{2}{x^2}[/tex] ......(1)
Substitute 0 for x in equation (1) to obtain the value of the function.
[tex]\begin{aligned}f\left( 0 \right)&= \frac{1}{2} \times{\left( 0 \right)^2}\\&= \frac{1}{2}\times0\\&=0\\\end{aligned}[/tex]
Substitute 1 for x in equation (1) to obtain the value of the function.
[tex]\begin{aligned}f\left( 1 \right)&=\frac{1}{2}\times {\left( 1 \right)^2}\\&=\frac{1}{2} \times1\\&= 0.5\\\end{aligned}[/tex]
Substitute -1 for x in equation (1) to obtain the value of the function.
[tex]\begin{aligned}f\left({ - 1} \right)&=\frac{1}{2}\times {\left( { - 1}\right)^2}\\&=\frac{1}{2} \times 1\\&=0.5\\\end{aligned}[/tex]
Substitute 2 for x in equation (1) to obtain the value of the function.
[tex]\begin{aligned}f\left( 2 \right)&=\frac{1}{2}\times {\left( 2 \right)^2}\\&= \frac{1}{2} \times 4\\ &=2 \\\end{aligned}[/tex]
Substitute for x in equation (1) to obtain the value of the function.
[tex]\begin{aligned}f\left({ - 2} \right)&= \frac{1}{2}\times {\left( { - 2}\right)^2}\\&=\frac{1}{2} \times 4\\&=2\\\end{aligned}[/tex]
Substitute 3 for x in equation (1) to obtain the value of the function.
[tex]\begin{aligned}f\left( 3 \right)&= \frac{1}{2} \times {\left( 3 \right)^2}\\&=\frac{1}{2}\times 9\\&= 4.5\\\end{aligned}[/tex]
Substitute for x in equation (1) to obtain the value of the function.
[tex]\begin{aligned}f\left( { - 3} \right)&=\frac{1}{2} \times {\left({ - 3} \right)^2}\\&=\frac{1}{2}\times 9\\&=4.5\\\end{aligned}[/tex]
Plot the points [tex]\left( {0,0} \right)[/tex] , [tex]\left( {1,0.5}\right)[/tex] ,[tex]\left( { - 1,0.5}\right)[/tex] ,[tex]\left( {2,2}\right)[/tex] ,[tex]\left( { - 2,2}\right)[/tex] , [tex]\left( { - 3,4.5}\right)[/tex] and [tex]\left( {3,4.5}\right)[/tex] on the graph.
Learn more:
1. Learn more about inverse of the function https://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 https://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.
