sketching curves(AS maths)?

Question

how should i go about solving this question?
please give me a thorough explanation because i'm really confused.

given that f(x)= 1/x, x≠0
sketch the graph of y=f(x)+3 and state the equations of the asymptotes.

(i'm not sure exactly what asymptotes are and what the ≠ symbol is supposed to mean)

Answer 1

Here.. I'll give you a start ...

x≠0 ====> "x not equal to zero"

f(x) = 1/x (given)

we need to sketch
y = f(x) + 3

y = 1/x + 3

How do you sketch this? We need values of y for different values of x

Lets make a table so we can plot this thing...

x| y = 1/x + 3
----------------------
-100 | 2.99
-50 | 2.98
-3| 2.666666667
-2| 2.5
-1| 2
0| (not defined for x = 0)
1| 4
2| 3.5
3| 3.333333333
50 | 3.02
100 | 3.01

Now, plot this on the graph

You should get two curves on either side of the y axis. This represents your y function.

Asymptotes, (garden variety def.) are like tangents to curves, except... they never touch the curves. E.g. If you plot f(X) = 1/x, you'll see that the curves approach the y axis but never touch it. So your y axis is an asymptote. And the equation of y axis is..... (guess?) .... well.. x= 0 .. because no matter where you are on the y axis, the x is always ... ? .. zero! (hint... There's also another asymptote)

Now that you have an idea of what asymptotes are.. can you see if there are asymptotes on this graph ?

Typically, textbooks explain the "limit method" (applying limits to functions) to obtain the asymptote equations. If you look around in the textbook for examples, you're bound to find that method. I'll leave that task for you :-)

Hope this helps.

Mahurshi Akilla

Answer 2

You should have learnt the shape of y = 1/x from your GCSE course. Now take a piece of graph paper and do a table of values from x = -6 to 6 in steps of 1 and plot the graph, using your calculator to calculate the y values. ( The table mode is useful here but, no doubt, you've thrown away the instruction leaflet.) You may note that you get an Ma Error when x = 0. This is because 1/0 is undefined. The symbol ≠ means is not equal to: the function is not defined for x = 0.

If you draw on your graph the lines x = 0 (the y-axis) and y = 0 (the x-axis), you will notice that the curve gets closer and closer to these lines but never actually touches. These lines are called the asymptotes.

Now go back to your table of values. Add 3 to each of the values for y. Plot this new graph, which has the equation:
y=f(x)+3

What has happened to the asymptotes. Write down their equations. [Hint: one hasn't changed.]

You really should be able to sort this out yourself. It's not a difficult question. Practise a few more similar questions, plotting the graphs, until you are happy that you fully understand this topic.

Answer 3

Order of attack: a million)ensure the area (because of the fact your radicand -- that expression under the unconventional sign -- ought to be 0 or greater). [ i'm getting a internet site of -- closed era: [0, 6] ]. 2) With one among those small area you need to do a factor for factor plot. [understand that the unfavourable sign makes all g(x) lie the two on or under the x-axis.] 3)although, you need to do what Ptolemy... has completed; then understand that your graph is basically the backside / decrease "a million/2" of the circle he describes, which include the criteria on the x-axis: (0, 0) and (6, 0).

Answer 4

Just draw the graph of 1/x that is going from infinity against Zero when x is growing from Zero up against infinity.

Then lift the function line with the value of 3, and then you have got it.

Answer 5

I'm glad I changed my mind about doing AS Maths. =|