A function's graph may include solutions that do not appear in its table of values.
a. true***
b. false
true
The correct answer is a. true.
When we graph a function, we plot points on a coordinate plane representing the function's input values (x) and output values (y). We connect these points to form a curve called the graph of the function.
A table of values, on the other hand, is a list that shows specific input-output pairs for the function. It provides a specific set of values to evaluate the function at.
The important thing to note is that a function's graph includes all the possible input-output combinations, not just the ones listed in the table of values. This means that there may be additional points on the graph that are not listed in the table.
For example, consider a quadratic function like f(x) = x^2. If the table of values only includes a few input-output pairs like (-2, 4), (0, 0), and (2, 4), it does not represent the entire graph. The graph of this quadratic function is a symmetric U shape and it includes infinitely many other points along the curve that are not listed in the table.
Therefore, a function's graph may include solutions that do not appear in its table of values, making the statement "a. true."