Math Problem Statement
For the piecewise function, find the values g(-4), g(3), and g(6). g(x) is defined as: g(x) = {x + 4, for x ≤ 3; 9 - x, for x > 3}.
Solution
We are given a piecewise function and need to find the values of , , and . The function is defined as:
x + 4 & \text{for } x \leq 3 \\ 9 - x & \text{for } x > 3 \end{cases}$$ ### Step 1: Find $$g(-4)$$ Since $$-4 \leq 3$$, we use the first case of the piecewise function: $$g(-4) = -4 + 4 = 0$$ ### Step 2: Find $$g(3)$$ Since $$3 \leq 3$$, we again use the first case: $$g(3) = 3 + 4 = 7$$ ### Step 3: Find $$g(6)$$ Since $$6 > 3$$, we use the second case of the piecewise function: $$g(6) = 9 - 6 = 3$$ ### Final Values: - $$g(-4) = 0$$ - $$g(3) = 7$$ - $$g(6) = 3$$ Would you like further clarification on any part of this process? Here are five related questions to deepen your understanding: 1. What happens if we define a new piecewise function for $$x > 6$$? 2. How would the function behave if we modified the conditions, for example, using $$x + 2$$ instead of $$x + 4$$? 3. Can you graph the piecewise function for $$x = -4$$ to $$x = 6$$? 4. How does the function change if we introduce another condition at $$x = 0$$? 5. What is the domain and range of this piecewise function? **Tip:** For piecewise functions, always check the condition associated with the input value carefully to select the correct function definition.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Linear Functions
Formulas
g(x) = x + 4 for x ≤ 3
g(x) = 9 - x for x > 3
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 8-10