Final answer:
The function y=4x+5 is a linear function and is continuous at all points on the real number line. There are no discontinuities, and it is defined for all real numbers.
Step-by-step explanation:
The function in question is y = 4x + 5. This is a linear function, and as such, it is continuous at all points on the real number line. Linear functions do not have breaks, holes, or jumps in their graph. They are defined for all real numbers, which means the function y = 4x + 5 is continuous for all values of x.
A linear function like this one doesn't have any discontinuities, so you won't find any value of x at which the function isn't continuous. Visually, if you were to plot this function on a graph by connecting points like (1, 5), (2, 10), (3, 7), and (4, 14), you would see that the function forms a straight line. However, these points do not actually lie on the line given by the equation y = 4x + 5, except for (1, 9), showing that there is an error in plotting them if this is the function in question. Rather, you should calculate the y-values using the given function.
When considering continuous probability functions and their properties mentioned, such as derivatives and areas under the curve, it is important to understand the distinction between these concepts and the straight line equation provided. Nonetheless, continuity in this context still refers to the absence of any disruptions in the value of the function as x varies over its domain.