The graph represents function 1 and the equation represents function 2:

A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3.

Function 2
y = 2x + 1

How much more is the rate of change of function 2 than the rate of change of function 1?

A.1
B.2
C.3
D.4

I say B.

slope 1 = (3-3)/(4-0) = 0

slope 2 = 2

2-0 = 2

To determine the rate of change of a function, we need to look at the slope of the line or the coefficient of x in the equation.

For function 1, we see that the line is a horizontal straight line, indicating that the slope is 0.

For function 2, we have the equation y = 2x + 1, where the coefficient of x is 2. This means that for every 1 unit increase in x, y increases by 2 units. Therefore, the rate of change for function 2 is 2.

To find the difference in the rate of change between the two functions, we subtract the rate of change of function 1 (0) from the rate of change of function 2 (2):

2 - 0 = 2

Therefore, the rate of change of function 2 is 2 units more than the rate of change of function 1.

So, your answer B is correct.

To find the rate of change of a function, we need to determine the slope of the function. In this case, let's start with Function 1, which is represented by a horizontal straight line in the graph.

Since the line is horizontal, it means that the y-coordinate (or the output) remains constant regardless of the change in the x-coordinate (or the input). In other words, there is no change in y for any change in x. Therefore, the rate of change (or slope) for Function 1 is 0.

Now let's move on to Function 2, which is represented by the equation y = 2x + 1. This equation is in the form of y = mx + b, where m is the coefficient of x and represents the slope.

In this case, the coefficient of x is 2. This means that for every unit increase in x, the corresponding value of y will increase by 2. Therefore, the rate of change (or slope) for Function 2 is 2.

Finally, to find the difference in the rate of change between Function 2 and Function 1, we subtract the rate of change of Function 1 (0) from the rate of change of Function 2 (2).

2 - 0 = 2

Hence, the rate of change of Function 2 is 2 more than the rate of change of Function 1. Therefore, the correct answer is indeed B.