Question 1
LEVEL 8
Plot the graph of y=sin(x) for -180^\circ\leq x\leq180^\circ.
Select the correct plot from the list below:
A:
B:
C:
D:
CORRECT ANSWER: D
WORKED SOLUTION:
Our usual graph for sin(x), between 0^\circ and 360^\circ looks a like this
And it repeats going backwards in a similar fashion, starting below the x-axis and then going above it. When the graph is restricted to being between -180^\circ\leq x\leq180^\circ it looks like:
Question 2
LEVEL 8
Plot the graph of y=tan(x) for -180^\circ\leq x\leq180^\circ.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: C
WORKED SOLUTION:
The tan graph has an asymptote at -90^\circ and -90^\circ, then again for every \pm180^\circ.
Furthermore, we have that tan(0^\circ)=0 and it gets smaller as it gets closer to -90^\circ and bigger as it gets closer to 90^\circ.
Finally, we just need to remember that the rest of the tan graph comes from the opposite ends of the asymptotes. So, if one goes towards the top, the next one comes from the bottom, and vice versa.
Question 3
LEVEL 8
Plot the graph of y=cos(x+360) for -180^\circ\leq x\leq180^\circ.
Select the correct plot from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
Our usual graph for cos(x), between 0^\circ and 360^\circ looks a like this
And continues in a similar fashion on the opposite side of the y-axis. As such, on -180^\circ\leq x\leq180^\circ, it looks like
But, how does this +360^\circ affect our graph? Well, we know that because it is in the function it will move the graph -360^\circ to the left. However, we know that that the graph of cos(x) repeats itself every 360^\circ, so our graphs looks exactly the same!
Question 4
LEVEL 8
Plot the graph of y=-sin(x) for 0^\circ\leq x\leq360^\circ.
Select the correct plot from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B
WORKED SOLUTION:
Our usual graph of y=sin(x) for 0^\circ\leq x\leq360^\circ.
However, we need to find y=-sin(x), which is a transformation of the form y=-f(x). But, we know that this just flips our graph in the x-axis, so it will have to look like this:
Question 5
LEVEL 8
Plot the graph of y=sin(-x) for -180^\circ\leq x\leq180^\circ.
Select the correct plot from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
Our usual graph of y=sin(x) for -180^\circ\leq x\leq180^\circ.
However, we need to find y=sin(-x), which is a transformation of the form y=f(-x). But, we know that this just flips our graph in the y-axis, so it will have to look like this:
