Find the function that has the greater rate of change
As x increases by 1, y increases by 3.
The graph has a line and 3 dots. the dots are labeled-
x: -1 | 0 | 1
y: 0 | 2 | 4
A. the slopes are equal
B. the graph has a greater slope
C. the function rule has a greater slope****
D. none of the above
1- the rates of change are equal
2- the slopes are equal
3- the function rule has greater slope
4- a parabola
5- graph b
6- -3,-2,1,6
these are 100% correct all the ones above here are the question answers for lesson 11 Comparing Function Unit 5: Functions
done. see earlier post.
To determine which function has the greater rate of change, we need to calculate the slopes of the lines represented by the given points. The slope of a line can be found using the formula:
slope (m) = (change in y) / (change in x)
Using the given points, we can calculate the slopes as follows:
For the line:
(x1, y1) = (-1, 0)
(x2, y2) = (1, 4)
slope_line = (y2 - y1) / (x2 - x1) = (4 - 0) / (1 - (-1)) = 4 / 2 = 2
For the three dots:
(x1, y1) = (-1, 0)
(x2, y2) = (0, 2)
slope_1 = (y2 - y1) / (x2 - x1) = (2 - 0) / (0 - (-1)) = 2 / 1 = 2
(x1, y1) = (0, 2)
(x2, y2) = (1, 4)
slope_2 = (y2 - y1) / (x2 - x1) = (4 - 2) / (1 - 0) = 2 / 1 = 2
Comparing the slopes:
slope_line = 2
slope_1 = 2
slope_2 = 2
The slope values for the line and the dots are all the same. Therefore, the answer is:
D. None of the above
To determine which function has the greater rate of change, we need to compare the slopes of the two functions.
In this case, we have three points on the graph: (-1, 0), (0, 2), and (1, 4). We can use these points to calculate the slope for the function.
The slope of a function is calculated using the formula: slope = (change in y) / (change in x). In this case, the change in x is always 1 since x is increasing by 1, and the change in y corresponds to the difference in y-values for each pair of points.
Let's calculate the slope for the given function:
For the points (-1, 0) and (0, 2), the change in y is 2 - 0 = 2. Dividing this by the change in x, which is 1, we get a slope of 2/1 = 2.
For the points (0, 2) and (1, 4), the change in y is 4 - 2 = 2. Dividing this by the change in x (which is again 1), we get a slope of 2/1 = 2.
Since both slopes are equal to 2, we can see that the slopes are equal. Therefore, the correct answer is A. The slopes are equal.
Therefore, the option C. The function rule has a greater slope is incorrect.