Find the Domain and Range y=-3/2sin(x/3+pi/6)+2

$y = - \frac{3}{2} \sin (\frac{x}{3} + \frac{π}{6}) + 2$

Step 1

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 2

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

Interval Notation:

$[\frac{1}{2}, \frac{7}{2}]$

Set-Builder Notation:

${y | \frac{1}{2} \leq y \leq \frac{7}{2}}$

Step 3

Determine the domain and range.

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

Range: $[\frac{1}{2}, \frac{7}{2}], {y | \frac{1}{2} \leq y \leq \frac{7}{2}}$

Step 4

Find the Domain and Range y=-3/2sin(x/3+pi/6)+2

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