True or False A function's graph may include solutions that do not appear in its table of values. (1 point) Responses true true false
True
False.
The correct response is TRUE.
To understand why this is true, let's break it down:
A function is a relation between a set of inputs (called the domain) and a set of outputs (called the range) such that each input is related to exactly one output. The graph of a function is a visual representation of how the inputs and outputs are related.
The table of values of a function lists some specific inputs along with their corresponding outputs. It is a way to organize the information and show a few examples of how the function behaves.
However, it is important to note that a function's graph is not limited to only the points included in its table of values. The graph represents all possible inputs and outputs of the function, both those that are explicitly listed in the table and those that are not.
Consider a simple example: the function y = x^2. Its table of values might only include a few specific points, such as (0,0), (1,1), and (2,4). However, the graph of this function is a parabola that continues infinitely in both directions. It includes all the points on the curve, including those not explicitly listed in the table of values.
So, the answer is true - a function's graph may include solutions that do not appear in its table of values.