State two types of functions that you know that do not have a maximum or a minimum when the domain is the set of all real numbers.
y = 5 x or any other linear function with finite slope
y = x^3 or any other odd power of x
Two types of functions that do not have a maximum or a minimum when the domain is the set of all real numbers are:
1. Constant functions: A constant function is a function where the output is always the same value, regardless of the input. For example, f(x) = 5 is a constant function that yields 5 for all real values of x. Since the output is constant, there are no maximum or minimum values.
2. Periodic functions: A periodic function is a function that repeats its values after a specific interval. Examples of periodic functions include sinusoidal functions like f(x) = sin(x) and f(x) = cos(x). These functions oscillate between -1 and 1 and repeat indefinitely. As there is no absolute highest or lowest point in their oscillation, they do not have a maximum or minimum over the entire real number domain.
Two types of functions that do not have a maximum or a minimum when the domain is the set of all real numbers are:
1. Constant function: A constant function is a function that always returns the same output, regardless of the input. For example, f(x) = 5. In this case, the function value is always 5, regardless of any real number x. Since there is no change in the function value, there is no maximum or minimum.
2. Linear function: A linear function is a function whose graph is a straight line. It can be represented in the form f(x) = mx + b, where m is the slope and b is the y-intercept. In a linear function, the slope determines the rate of change, and there are no restrictions on how large or small the function value can be. As a result, linear functions do not have a maximum or minimum when the domain is the set of all real numbers.