Question

Evaluate f(-5), f(0), and f(3) for the piecewise defined function.

Answer 1

Without the details of the piecewise function, it is impossible to evaluate f(-5), f(0), or f(3). Generally, evaluating a piecewise function involves applying the specific rule for the interval that contains the input value, but the lack of function information here precludes a specific answer.

Step-by-step explanation:

The student has asked about evaluating a piecewise defined function at specific inputs; however, the function itself is not provided in the question, making it impossible to give an exact answer.

Typically, to evaluate a piecewise function like f(-5), f(0), and f(3), you would need to look at the definition of the function and see which piece of the function is applicable for the values of x mentioned. Without the function details, this specific question cannot be answered.

In general, a piecewise function will have different rules for different intervals of x. If the function were provided, you would identify the correct interval for each input value, plug the input into the rule defined for that interval, and compute the result.

For example, if a function is defined as f(x) = x² for x < 0 and f(x) = 2x + 3 for x ≥ 0, then f(-5) would be computed using the x² rule resulting in 25, f(0) using the 2x + 3 rule resulting in 3, and f(3) using the 2x + 3 rule resulting in 9.

Answer 2

Without the explicit definition of the piecewise function, we cannot evaluate f(-5), f(0), and f(3). Steps to evaluate piecewise functions are described along with the appearance of positive, negative, and zero slopes.

Step-by-step explanation:

Evaluating a piecewise-defined function, such as f(x), involves determining which piece of the function applies at the given values of x and then computing the function's value for those specific points. Unfortunately, without the explicit definition of the piecewise function, we cannot calculate exact values for f(-5), f(0), and f(3). However, we can discuss how to approach this evaluation in general terms.

First, you would need to look at the intervals defined by the piecewise function and determine which interval each value of x falls into. For example, if you have a function defined one way for x less than 0 and another way for x greater than or equal to 0, you would use the first definition for f(-5) and the second for f(0) and f(3). Then, you would insert the specific value of x into the correct piece of the function and simplify to find the result.

Positive slope indicates that as x increases, f(x) also increases. A negative slope means that as x increases, f(x) decreases. A slope of zero suggests that f(x) remains constant regardless of changes in x. Understanding the concept of slopes is important when graphing or evaluating functions.