How to sketch the graph of a function?

Question

Hello

Can someone explain to me, in very simple terms, how to "sketch the graph" of a function. The questions I have to do all have 'log' in them so I guess that means they're all "logarithmic functions"? Heh.

Anyway one of the questions is: y = -8 log₄ x/2

(that's y equals negative 8 log to base 4 x over 2)

Thanks in advance! (I'm rubbish at math)

Answer 1

That's not an easy one!

The general method of doing this is

- Choose some values for x,

- for each one, calculate the corresponding value of y.

- Plot the point (x,y), meaning put a dot at point (x,y).

- Connect the dots.

You need enough points to get an idea what the graph looks like.

A good way to start is to find some examples which are similar

to the function  you have to graph, which will give you an idea

of good x values to choose.

The sooner the overall curve starts to take shape,

the fewer points you have to choose.

In this case, I would make the initial points easy to calculate,

so choose values of x to be powers of 4 times 2:

Powers of 4 are 1, 4, 16, 64, 256

Double those gives 2, 8, 32, 128, 512

Log base 4 of x/2 is then 0, 1, 2, 3, 4

Multiply by -8: 0, -8, -16, -24, -32

So you have the points

(2,0) (8,-8) (32,-16) (128,-24) (512,-32)

which are rather spread out.

But you can see that the curve is

steep near the y-axis, crosses the x-axis at (2,0)

then flattens out as it continues to the right.

If you want some more intermediate points,

calculate 4^(some intermediate powers)

for example, 4^(1.5) = 4*sqrt(4) = 8, so choose x = 16.

16/2 = 8, log base 4 (8) = 1.5, 1.5 * -8 = -12,

so you have the point (16,-12).

Good luck!

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