If m<0 and b>0,the graph of y=max+b does not pass through which quadrant
2 answers:
Answer: Quadrant III
Explanation:
Let's pick example values for m and b
I'll go for m = -2 and b = 5. Anything works as long as m is negative and b is positive.
We go from y = mx+b to y = -2x+5
Plot this graph as shown below. The line passes through quadrants I, II, and IV. Only quadrant III is not touched at all.
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Part A:
The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:
and
are points on the function
You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:
Now, let's find the slopes for each of the sections of the function:
<u>Section A</u>
<u>Section B</u>
Part B:
In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.
It is 25 times greater. This is because is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.