Coursera.6.502.Graphs of functions and kinematics summative quiz
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1. Mathematics for Computer Science
2. Week 6
3. 6.502 Graphs of functions and kinematics summative quiz
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1.
Question 1
If you were to plot the point (7,1)(7,1) what would be the correct method?
Select the two options that complete the blank spaces in the following statement:
'Starting from the origin ________ and ________'
1 / 1 point
Move 77 units down in the vertical direction
Move 11 unit to the left in the horizontal direction
Move 11 unit to the right in the horizontal direction
Move 11 unit up in the vertical direction
Move 11 unit down in the vertical direction
Move 77 units to the right in the horizontal direction
Move 77 units to the left in the horizontal direction
Move 77 units up in the vertical direction
2.
Question 2
Write the condition that describes the interval for values of �x:
[−25,6][−25,6].
Notation:
Use <= for the ≤≤ symbol
Use >= for the ≥≥ symbol
For example:
to represent 2≤�<52≤x<5, simply write
2<=x<5
with no spaces between characters.
1 / 1 point
-25<=x<=6
3.
Question 3
Write the interval notation for the condition:
−7≤�<11−7≤x<11.
Notation:
use brackets (,),;
use '+infinity' to denote +∞+∞;
use '-infinity' to denote −∞−∞.
Enter the answer without any spaces, for example to enter [�,�)[a,b) you would type:
[a,b)
1 / 1 point
[-7,11)
4.
Question 4
Consider the function �(�)=−2(−5−�)2f(x)=(−5−x)2−2. Prepare a table of values to plot the graph of �(�)f(x).
Select all statements which reflect essential aspects to consider when preparing the table of values for this function.
Select all statements which reflect essential characteristics always observed in such table of values.
1 / 1 point
Include more values of �x close to −5−5 than around any other number
this is essential for displaying the behaviour near −5−5; what is the behaviour near −5−5?
The domain of this function is �−5R−5
None of the other options apply
The graph has a vertical asymptote at �=5x=5
Include positive and negative values of �x
it is important to report the behaviour of the function as �x tends to infinity on both ends
The domain of this function is �−−5R−−5
the denominator is 00 when �=−5x=−5 so we exclude this value from the domain
The graph has a vertical asymptote at �=−2x=−2
Include values of �x symmetrical with respected to 55
The graph has a horizontal asymptote at �=0y=0
in future topics you will learn how to prove this statement using limits
the graph has a vertex at (5,0)(5,0)
The graph has a vertical asymptote at �=−5y=−5
The table will show more values of �y close to 00 than around any other number
you can verify this yourself, for your own learning note down the reason for this
Cannot calculate the function for �=0x=0
5.
Question 5
Consider the function �(�)=�2+6�+9f(x)=x2+6x+9. Prepare a table of values to plot the graph of �(�)f(x).
Select all statements which reflect essential aspects to consider when preparing the table of values for this function.
Select all statements which reflect essential characteristics always observed in such table of values.
1 / 1 point
The graph has a vertex at (6,9)(6,9)
The graph of �(�)f(x) has a vertex at (3,0)(3,0)
The graph has a vertical asymptote at �=−3x=−3
The table will show positive and negative values of �y
None of the other options apply
The graph of �(�)f(x) has a vertex at (−3,0)(−3,0)
this function can be rewritten as �(�)=(�+3)2f(x)=(x+3)2
Rewrite the expression of �(�)f(x) by 'completing the square' in order to find the coordinates of the vertex
Include more values of �x close to 00 than around any other number
Include values of �x symmetrical with respect to 33
Include positive and negative values of �x
Include many more values of �x close to 33 than around any other number
Include many more values of �x close to −3−3 than around any other number
this will help with plotting the shape of the graph near the vertex more accurately
6.
Question 6
In an attempt to plot the graph of the function �(�)=1�2f(x)=x21 a learner produced the graph below:
The 'crosses' mark points that were plotted from a table of values.
The orange line is the intended graph.
You are to assess if this graph correctly represents �(�)f(x) and if the table of values used is adequate.
You are to assess which important features are represented by this graph and which ones are missing.
Select all statements that apply.
0 / 1 point
this graph does not portrait the behaviour of the function for �x between −1−1 and 11
This is a negative aspect of the graph and table of values: there are many ways of completing the graph between −1−1 and 11 so this graph is not an accurate description of the function
None of the other options is correct
the asymptotes are clearly marked in the graph
the orange line is a smooth curve through the points instead of joining up the points with straight-lines
the graph touches the �y-axis
the graph correctly represents �(�)f(x)
from the graph it is possible to understand that the line of equation �=0y=0 is an asymptote of the graph
This is a positive aspect of the graph and table of values: the graph appears to approximate the �x-axis as �x is greater than 6 and lesser than -6
the asymptotic behaviour near �=0x=0 is not portrayed in the plot
the choice of window for the graph does not fully portray the behaviour of the function
the graph touches the �x-axis
from the graph it is possible to understand that the line of equation �=0x=0 is an asymptote of the graph
7.
Question 7
What is wrong with this plot and table of values:
x=y=−50.04−40.06−30.11−20.25−111120.2530.1140.0650.04
Select all statements that are true.
1 / 1 point
the asymptotes are missing
This is negative aspect of the graph.
the graph excludes the behaviour for �>6x>6 and for �<−6x<−6
This is a negative aspect of the graph. The graph should be continued.
it shows the maximum and minimum values of the function
the table of values is fine as the values are equally spaced
the graph is wrong because it excludes the zeros of the function
the graph is incomplete as the points (−1,1)(−1,1) and (1,1)(1,1) should be joined up to make continuous line
the graph excludes the behaviour of the function between �=−1x=−1 and �=1x=1
This is a negative aspect of the graph. The graph and table of values need to be completed.
the graph of this function should not have asymptotes
the table of values is incomplete because �=0x=0 is missing
the graph is wrong because it does not show the intercept
nothing is wrong, it is a fair plot as it shows all the points calculated
8.
Question 8
Choose all that apply:
�=1�2+�y=x2+x1 is transformed to �=−7+1(�−8)2+�−8y=−7+(x−8)2+x−81
1 / 1 point
A translation by +7+7 units in the �x direction
A translation by +8+8 units in the �y direction
A translation by −7−7 units in the �y direction
A scaling by a factor of 77 in the �y direction
A scaling by a factor of 88 in the �x direction
A translation by +7+7 units in the �y direction
A translation by +8+8 units in the �x direction
Ascaling by a factor of 1771 in the �y direction
A scaling by a factor of 1881 in the �y direction
A scaling by a factor of 77 in the �x directio
A scaling by a factor of 88 in the �y direction
A translation by −8−8 units in the �y direction
A translation by −7−7 units in the �x direction
A scaling by a factor of 1881 in the �x direction
A scaling by a factor of 1771 in the �x direction
