Question

In Exercises 31–32, the domain of each piecewise function is (-∞, ∞) (a) Graph each function. (b) Use the graph to determine the function's range.

Accepted Answer

Understand the problem: A piecewise function is defined by different expressions depending on the input value (x). The domain is given as (-∞, ∞), meaning the function is defined for all real numbers. We need to graph the function and determine its range based on the graph. Step 1: Identify the pieces of the piecewise function. For each piece, note the expression and the interval of x-values where it applies. For example, if the function is defined as f(x) = $$x^2$$ for x \u003c 0 and f(x) = x + 1 for x ≥ 0, these are the two pieces to graph. Step 2: Graph each piece of the function separately. For each piece, plot points by substituting x-values into the corresponding expression. Be mindful of whether the endpoints of the intervals are included (closed circle) or excluded (open circle). Step 3: Combine the graphs of all pieces into a single graph. Ensure the transitions between pieces are accurate and consistent with the domain restrictions for each piece. Step 4: Analyze the graph to determine the range of the function. The range is the set of all y-values that the function takes on. Look at the graph to see the lowest and highest y-values (if any) and whether the function covers all values in between.

In Exercises 31–32, the domain of each piecewise function is (-∞, ∞) (a) Graph each function. (b) Use the graph to determine the function's range.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Piecewise Functions

Graphing Functions

Range of a Function