Find the Domain and Range 2x^2+y=8x-6

$2 x^{2} + y = 8 x - 6$

Step 1

Subtract $2 x^{2}$ from both sides of the equation.

$y = 8 x - 6 - 2 x^{2}$

Step 2

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 3

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

Interval Notation:

$(- \infty, 2]$

Set-Builder Notation:

${y | y \leq 2}$

Step 4

Determine the domain and range.

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

Range: $(- \infty, 2], {y | y \leq 2}$

Step 5

Find the Domain and Range 2x^2+y=8x-6

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