[tex]\dfrac{3}{2}\ \text{represents the amplitude of the graph.}\\\\\text{Which means the maximum is }\dfrac{3}{2}\ \text{and the minimum is }-\dfrac{3}{2}.\\\\\text{The -1 at the end of the equation shifts the maximum and minimum}\\\text{down 1 unit. So the new maximum is }\dfrac{3}{2}-1=\dfrac{1}{2}\\\\\text{and the new minimum is }-\dfrac{3}{2}-1=-2\dfrac{1}{2}\\\\\implies \large\boxed{\text{The range is }-2\dfrac{1}{2}\leq y \leq \dfrac{1}{2}}[/tex]
