Explanation:
To identify a linear function, you can look for the following characteristics:
1. Constant Rate of Change: In a linear function, the rate of change between any two points on the graph of the function remains constant. This means that as the input (x) increases or decreases by a certain amount, the output (y) also changes by a consistent amount. For example, if the function represents the cost of a product, a linear function would show that for every one unit increase in quantity, the cost increases or decreases by a fixed amount.
2. Straight Line: The graph of a linear function is a straight line. It means that when you plot the points on a coordinate plane, they will form a straight line rather than a curve or a bend. If the points do not align in a straight line, then it is not a linear function.
3. No Exponents: In a linear function, the variables (x and y) are raised only to the first power (exponent 1). This means that you will not see variables squared, cubed, or raised to any other exponent in a linear function. For example, a linear function could be written as y = 3x + 2, where x is raised to the first power.
4. Absence of Other Functions: A linear function only includes the variables x and y, without the presence of other functions such as square roots, trigonometric functions, or logarithmic functions. These additional functions would indicate a non-linear relationship.
By examining these characteristics, you can determine if a given function is linear or not. Remember to analyze the rate of change, the shape of the graph, the exponents of the variables, and the absence of other functions.
I hope this helps :)