Algebra Examples

$y^{2} = x^{2}$

Step 1

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| y | = | x |$

Step 2

Solve for $y$ .

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Step 2.1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$y = \pm | x |$

Step 2.2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.2.1

First, use the positive value of the $\pm$ to find the first solution.

$y = | x |$

Step 2.2.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - | x |$

Step 2.2.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = | x |$

$y = - | x |$

$y = | x |$

$y = - | x |$

$y = | x |$

$y = - | x |$

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:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

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

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6