In order to identify the input and output of a function, you will need to look at the function's equation or expression. The input is the value that is plugged into the function, typically represented by the variable x. The output is the result of the function, represented by the variable y or f(x).
The steps to solve a function depend on the type of function and the specific problem you are trying to solve. Generally, you will need to plug in the given input value for the variable x, solve for the output value using the function's equation or expression, and then check your solution by substituting it back into the equation. It is also important to follow the correct order of operations when solving the function.
To graph a function, you will need to plot points on a coordinate plane. The x-coordinates will represent the input values, and the y-coordinates will represent the output values. You can also use the function's equation to identify key points on the graph, such as the y-intercept and any intercepts with the x-axis. Once you have plotted enough points, you can connect them to create a line or curve that represents the function.
Linear functions have a constant rate of change, meaning the output changes by the same amount for every unit change in the input. This results in a straight line when graphed. Nonlinear functions, on the other hand, have a varying rate of change and do not result in a straight line when graphed. They can take on different shapes, such as curves or exponential growth/decay.
Functions are used to model many real-life situations, such as calculating the cost of a phone plan based on the number of minutes used, or predicting the growth of a population over time. By understanding how to solve and graph functions, you can apply this knowledge to make predictions and solve problems in various fields, including science, finance, and engineering.