Problem 68 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The only nongraphic method that I have for evaluating a function at a given value is to substitute that value into the function's equation.

Step-by-Step Solution

Answer

The statement does not make sense. While substitution is indeed a nongraphic method to evaluate a function, it is not the only one. Other nongraphic methods exist like using tables, case by case analysis, or solving the function's equation algebraically.

Step 1: Analysing the statement

The first step is to analyze the given statement. Here, it is saying that the only method to evaluate a function at a specific value, other than graphically, is to substitute that value into the function's equation. This implies the assumption that there are no other ways apart from graphical and substituting directly into the function's equation, which needs to be verified.

Step 2: Checking if the substituting method is a valid nongraphic method

By definition, a function is a rule that assigns to each input exactly one output. The output is the value of the function, which can be found by substituting the input value into the function. This makes it clear that substituting the input value into the function's equation is indeed a valid method to evaluate the function. It is also a nongraphic method as it doesn't involve any graphical visualization of the function.

Step 3: Considering other non-graphical methods

While substituting values directly into the function's equation is a valid method, it is not the only nongraphic method to evaluate a function. There are other methods like using tables, case by case analysis, or solving the function's equation using algebraic methods. Thus the statement that substitution is the only nongraphic method is not accurate.