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

May 17, 2018

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

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

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

#### Explanation:

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Consider the function given:

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

color(green)("Step 1 :"

Create a data table as shown: $x \mathmr{and} y$ 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 $\left(x , y\right)$ 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. 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.