How do you find the domain and range of #y=3x^2#?

1 Answer
May 17, 2018

Answer:

#" "#
For the given function: #color(blue)(y-3x^2# :

Domain : #color(red)(-oo < x < oo#

Range : #color(red)(f(x) >= 0#

Explanation:

#" "#
Consider the function given:

#color(red)(y=f(x)=3x^2#

#color(green)("Step 1 :"#

Create a data table as shown:

enter image source here

#x and y# values are available both for the Parent function and the given function.

When we graph, it will help to understand the presence of a numeric value as the coefficient of the #x^2# term and its influence on the shape of the graph.

#color(green)("Step 2 :"#

The Domain of a function is all possible input values that are used to manipulate to produce an output or result.

The function must also be defined for these values.

For the given function #color(red)(y=f(x)=3x^2#, there are no constraints for the #x# values.

Hence,

Domain : #color(red)(-oo < x < oo#

#color(green)("Step 3 :"#

Range refers to the set of #y# values in the #(x,y)# coordinate pair for which the function is well-defined.

Hence,

Range : #color(red)(f(x) >= 0#

#color(green)("Step 4 :"#

Examine the graph to visually verify, the results obtained for domain and range.

enter image source here

Note that the graph for the Parent function #color(blue)(y=f(x)=x^2# is also a part of the graph.

Hope it helps.