Subjects algebra

Piecewise Evaluation 0B5371

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1. **State the problem:** We have a piecewise function defined as: $$ g(x) = \begin{cases} -2 & \text{if } -2 \leq x < -1 \\ -1 & \text{if } -1 \leq x < 0 \\ 0 & \text{if } 0 \leq x < 1 \\ 1 & \text{if } 1 \leq x < 2 \end{cases} $$ We need to find the values of $g(-1)$, $g(0.25)$, and $g(1)$. 2. **Recall how to evaluate piecewise functions:** To find $g(a)$, determine which interval $a$ belongs to and use the corresponding function value. 3. **Evaluate $g(-1)$:** Since $-1$ satisfies $-1 \leq x < 0$, we use $g(x) = -1$. $$g(-1) = -1$$ 4. **Evaluate $g(0.25)$:** Since $0.25$ satisfies $0 \leq x < 1$, we use $g(x) = 0$. $$g(0.25) = 0$$ 5. **Evaluate $g(1)$:** Since $1$ satisfies $1 \leq x < 2$, we use $g(x) = 1$. $$g(1) = 1$$ **Final answers:** $$g(-1) = -1, \quad g(0.25) = 0, \quad g(1) = 1$$