Find the function that has the greater rate of change
As x increases by 1, y increases by 3.
The graph-
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
Well, it seems we have an equation face-off! In one corner, we have a rate of change where for every increase of 1 in x, y increases by 3. And in the other corner, we have a graph that goes from (0,2) to (1,4).
Now, let's take a closer look at the graph. From (0,2) to (1,4), we can see that for an increase of x by 1, y increases by 2.
Hmm, it seems like the second corner is quick with numbers! The slope of the graph is 2, while the first corner boasts a slope of 3. Sigh, poor first corner. So, the correct answer is D. None of the above since the slopes are not equal and the function rule does not have a greater slope.
The correct answer is C. the function rule has a greater slope.
In the given graph, as x increases by 1, the corresponding y-values increase by 2 (from 0 to 2) for the second point and by 2 again (from 2 to 4) for the third point. Thus, the rate of change of y with respect to x is 2/1, or simply 2.
In the statement, it is mentioned that as x increases by 1, y increases by 3. This means that the rate of change of y with respect to x is 3/1, or simply 3.
Since 3 > 2, it follows that the function rule has a greater slope.
To find the function that has the greater rate of change, we will compare the slopes of the two functions.
In this case, we are given a graph with three points, (-1, 0), (0, 2), and (1, 4). To find the slope of a function, we can use the formula:
slope = (change in y) / (change in x)
Let's calculate the slope for the given points:
For the first function:
Change in x = 1 - 0 = 1
Change in y = 2 - 0 = 2
Slope = (2 - 0) / (1 - 0) = 2/1 = 2
For the second function:
Change in x = 1 - (-1) = 2
Change in y = 4 - 0 = 4
Slope = (4 - 0) / (2 - 1) = 4/1 = 4
Comparing the slopes, we see that the slope for the second function (C. the function rule has a greater slope) is greater than the slope for the first function (A. the slopes are equal). Therefore, the correct answer is C. the function rule has a greater slope.
Only the graph of a function has a slope. This and similar questions are extremely poorly worded.
y has a greater rate of change. There is only one slope: that of the function. Its slope is 3.
Only the function has a slope. x and y do not have slopes. They just have rates of change. The slope tells you which variable changes faster.
This question is posed in pseudo-mathematical gibberish. It should be more like
Find the variable that has the greater rate of change
As x increases by 1, y increases by 3.
The graph-
x: -1 | 0 | 1
y: 0 | 2 | 4
A. the rates are equal
B. x has a greater rate of change
C. y has a greater rate of change
D. none of the above
Since C is correct, the slope is greater than 1.