Questions: Suppose that the function h is defined on the interval (-2.5,1.5) as follows. h(x) = -2 if -2.5 < x ≤ -1.5 -1 if -1.5 < x ≤ -0.5 0 if -0.5 < x < 0.5 1 if 0.5 ≤ x < 1.5 Find h(-1.5), h(-0.9), and h(0.5). h(-1.5)= h(-0.9)= h(0.5)=

Solution Steps

To find the values of the function \( h \) at specific points, we need to determine which interval each point falls into and then use the corresponding function value for that interval. For \( h(-1.5) \), \( h(-0.9) \), and \( h(0.5) \), we will check each point against the defined intervals and assign the appropriate value.

To find \( h(-1.5) \), we check which interval \( -1.5 \) falls into. According to the definition of \( h \): \[ h(-1.5) = -2 \quad \text{(since } -2.5 < -1.5 \leq -1.5\text{)} \]

Next, we evaluate \( h(-0.9) \). The point \( -0.9 \) falls into the interval: \[ h(-0.9) = -1 \quad \text{(since } -1.5 < -0.9 \leq -0.5\text{)} \]

Finally, we evaluate \( h(0.5) \). The point \( 0.5 \) falls into the interval: \[ h(0.5) = 1 \quad \text{(since } 0.5 \leq 0.5 < 1.5\text{)} \]

Final Answer