Compare the two functions:
Function 1:
x 0 1 2 3 4 5
y -20 -5 10 25 40 55
Function 2:
(4 points)
Which function has the larger y-intercept?
Which function has a constant rate of change?
Which function has the greater rate of change in the interval [0,2]?
Which function has the greater rate of change in the interval [4,5]?
To compare the two functions:
Function 1: y = 15x - 20
Function 2: y = 10x
1. Function 1 has a y-intercept of -20, while Function 2 has a y-intercept of 0. Therefore, Function 1 has the larger y-intercept.
2. The rate of change for Function 1 is 15, as the coefficient of x is 15. This means that the function has a constant rate of change. Function 2 also has a constant rate of change of 10, as the coefficient of x is 10.
3. To find the rate of change in the interval [0,2], we calculate the change in y divided by the change in x for each function:
Function 1: (10 - (-20)) / (2 - 0) = 30 / 2 = 15
Function 2: (20 - 0) / (2 - 0) = 20 / 2 = 10
Therefore, Function 1 has the greater rate of change in the interval [0,2].
4. To find the rate of change in the interval [4,5]:
Function 1: (55 - 40) / (5 - 4) = 15 / 1 = 15
Function 2: (50 - 40) / (5 - 4) = 10 / 1 = 10
Therefore, Function 1 has the greater rate of change in the interval [4,5].