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? (5 points)
Group of answer choices
1
2
3
4
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To compare the rate of change of Function 2 (y = 2x + 1) and Function 1 (represented by the horizontal line), we need to find the slopes of both functions.
The slope of a straight line can be found using the formula:
slope = (change in y) / (change in x)
Function 1:
Since the line is horizontal, the change in y (rise) is 0, and the change in x (run) is 4 - 0 = 4.
slope of Function 1 = 0/4 = 0
Function 2:
The equation y = 2x + 1 is in the form y = mx + b, where m is the slope. Therefore, the slope of Function 2 is 2.
Now let's compare the slopes:
The rate of change of Function 2 (slope = 2) is 2 units for every 1 unit change in x.
However, the rate of change of Function 1 (slope = 0) is 0 units for every 1 unit change in x.
Therefore, the rate of change of Function 2 is 2 units greater than the rate of change of Function 1.
The correct answer is 2.