Question

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

Answer 1

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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 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.

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.