Questions: The domain of the piecewise function is (-∞, ∞). a. Graph the function. b. Use your graph to determine the function's range. f(x) = -4x if x ≤ 0 -4 if x > 0 a. Choose the correct graph below. A. B. C. D. b. The range of f(x) is . (Type your answer using interval notation, set notation, and the union operator as needed.)

Solution Steps

The given piecewise function is: \[ f(x) = \begin{cases} -4x & \text{if } x \leq 0 \\ -4 & \text{if } x > 0 \end{cases} \]

• For \( x \leq 0 \), the function is \( f(x) = -4x \). This is a linear function with a slope of -4.
• For \( x > 0 \), the function is \( f(x) = -4 \). This is a constant function.

• The graph should show a line with a slope of -4 for \( x \leq 0 \) and a horizontal line at \( y = -4 \) for \( x > 0 \).
• The correct graph is option C.

• For \( x \leq 0 \), as \( x \) approaches negative infinity, \( f(x) \) approaches positive infinity.
• For \( x > 0 \), \( f(x) = -4 \).

Final Answer