The instantaneous rate of change of g(x) is the same for every real value of x. What type of function is g(x)?

constant slope is a straight line

If the instantaneous rate of change of g(x) is the same for every real value of x, then g(x) is a linear function. A linear function has a constant rate of change, meaning that the slope (rate of change) remains the same for all values of x.

To determine the type of function that g(x) represents, we need to consider the condition given: the instantaneous rate of change of g(x) is the same for every real value of x.

A function that has a constant rate of change for every real value of x is a linear function. In other words, if the slope of a function is constant, the function represents a linear relationship.

To verify this, you can take the derivative of g(x) and observe if it is a constant value. If the derivative is constant, then the function is linear.

Alternatively, you can also graph the function g(x) to see if it produces a straight line. If the graph is a straight line, then g(x) is a linear function.