Graph of functions

algray09

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May 12, 2020
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I’m confused how to start step a, all I know is that they intercept each other. Does the formulas involve the v and h? And step b there isn’t a f(t) labeled on the graph so I’m confused where to start on that.
57334E9C-D851-4780-B520-0DDFCB903CB6.jpeg
 
Also step C wants the average rate of change of M on interval [0,0.5]. I know the formula for average rate of change is f(x+h)-f(x)/h. Do I use the formula for m from part a and use the numbers from interval?
 
Both the red and blue lines are meant to be straight lines (otherwise part a is insoluble).

How do you determine the equation representing a straight line between two given points (you learned this in first-year algebra)?

What is the dependent variable?

What is the independent variable?

So what are the two equations?
 
You are asked to find the equation of two (linear) functions. How you find the equation of that line does not depend on the other function.

Suppose I draw a line and the equation of that line is y=22x-11. Now if I happen to draw another line that crosses (or doesn't cross) that line, the equation of the line is y=22x-11.

Each curve that has a function associated with it does not change just because you draw another curve. You must think about that and clearly understand what I am saying before you move on.
 
I’m confused how to start step a, all I know is that they intercept each other. Does the formulas involve the v and h? And step b there isn’t a f(t) labeled on the graph so I’m confused where to start on that.
View attachment 34038
As for v and h, v is the variable on the vertical axis, meaning velocity; what they graphed at v = M(t) and v + C(t). The equations you write will probably not mention v. On the other hand, h is just the unit, "hours". The variable is called t.

As for f, you're right that no function in the problem is called f. My guess is that the question is generic: explain the meaning and units of the slope of either function, M or C.
Also step C wants the average rate of change of M on interval [0,0.5]. I know the formula for average rate of change is f(x+h)-f(x)/h. Do I use the formula for m from part a and use the numbers from interval?
The average rate of change for a line is indeed the slope you use in your equation; but they are explicitly asking you to calculate the average rate of change from its definition, and confirm that. So just find the values of M(0) and M(0.5) and use them in the formula. (The formula you need is not really the one you show, though it can be adapted. You should have a formula for the rate of change over an interval from a to b.)
 
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