Precalculus Examples

$x^{2} = 3 y$

Step 1

Rewrite the equation as $3 y = x^{2}$ .

$3 y = x^{2}$

Step 2

Divide each term in $3 y = x^{2}$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 y = x^{2}$ by $3$ .

$\frac{3 y}{3} = \frac{x^{2}}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{x^{2}}{3}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{x^{2}}{3}$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Step 5

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $[0, \infty), {y | y \geq 0}$

Step 6