-apc.4.2.9 graph of f(x) to g(x)

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In summary: PDF Portable Document FormatAP Advanced PlacementIn summary, the conversation discusses a problem involving graphs and integrals, where the correct answer is determined by observing the curvature of the graph and the slope of the original function. The conversation also mentions a work in progress PDF document and a goal to reach 100 problems.
  • #1

karush

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Screenshot 2020-09-30 at 1.04.05 PM.png

image due to graphsok just by observation I chose D since integrals tend to introduce curves not eliminate them and the slope was positive
 
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  • #2
two significant typos in this problem ...

(1) should be $\displaystyle g(x) = \int_2^x f(t) \, dt$,

(2) which of the following could be $y=g(x)$, not $g(f)$

$g’(x) = f(x) \implies$ the graph of $f(x)$ is the graph of the derivative of $g(x)$

so ... what do you think?
 
  • #3
good catch
 
  • #4
karush said:
https://www.physicsforums.com/attachments/10736
image due to graphsok just by observation I chose D since integrals tend to introduce curves not eliminate them and the slope was positive
You should be able to say much more than that! Since the graph of f is a straight line, f is "linear" and its integral is quadratic so its graph is a parabola. Further since the graph of f is below the x-axis the integral starts out negative and becomes positive. Yes, the slope of f is positive so the curvature of g is positive. THAT is why "D" is the correct choice!
 
  • #5
deriv_analysis2.jpg
 
  • #6
graphs always help a lot
 
  • #7
Here is a WIP of a PDF of the MHB replies to the AP Calculus problems given here
A counter has been put into the overleaf document which at this posting is 40,000 views of the replies
My goal is to make the PDF error free and reach 100 problems
Mahalo
https://dl.orangedox.com/6rStfn4eMFHuHvAKuX
 
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  • #8
"WIP', "PDF", "AP"? I thought we were supposed to use English on this site!
 
  • #9
WIP Work In Progress
 
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What is the meaning of "-apc.4.2.9 graph of f(x) to g(x)"?

The term "-apc.4.2.9 graph of f(x) to g(x)" refers to a graph that shows the relationship between two functions, f(x) and g(x), with a specific transformation applied to the graph of f(x).

How is the graph of f(x) to g(x) created?

The graph of f(x) to g(x) is created by applying a transformation to the graph of f(x), such as a translation, reflection, or dilation. This transformation is represented by the "-apc.4.2.9" notation.

What does the "-apc.4.2.9" notation mean?

The "-apc.4.2.9" notation is used to represent the specific transformation that is applied to the graph of f(x) to create the graph of f(x) to g(x). The letters "a", "p", and "c" stand for the type of transformation (a for dilation, p for reflection, c for translation), and the numbers "4" and "2" represent the direction and amount of the transformation.

What information can be determined from the graph of f(x) to g(x)?

The graph of f(x) to g(x) can provide information about the relationship between the two functions, such as whether they are inverses of each other or if one is a transformation of the other. It can also show the specific transformation that was applied to the graph of f(x) to create the graph of f(x) to g(x).

How can the graph of f(x) to g(x) be used in mathematical analysis?

The graph of f(x) to g(x) can be used to study the properties and behavior of the two functions, f(x) and g(x). It can also be used to make predictions and solve equations involving the two functions. Additionally, it can help in understanding the concept of transformations and their effects on functions.

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