Question

Not all functions are expressed as equations. Here is a graph

of a function g. The equation is not given, but you can still use
function notation to express the outputs for various inputs.

Answer 1

Graphs are essential in mathematics for visually expressing equations and displaying data by plotting (x,y) data pairs, revealing the relationship between variables even without an explicit equation.

Step-by-step explanation:

Expressing Equations Graphically

Graphs serve as a pivotal tool in mathematics, particularly when it comes to expressing equations visually and displaying sets of data. For instance, when we consider the value of y changing as a function of x, different values of x correspond to various values of y. This correlation can be visualized with a graph, which is a representation of specific (x,y) data pairs. Without the actual equation, we can still discuss the behavior of the function graphically by analyzing the plotted points where each represents an input-output pair, i.e., the x-coordinate represents the input, while the y-coordinate corresponds to the output of the function at that particular x-value.

The use of a graph allows us to determine outputs for specific inputs by examining where the input value on the x-axis corresponds to the output value on the y-axis. This can often become a visually intuitive task, as opposed to dealing with complex equations.

Answer 2

The image has all the answers to your question.