Sketch graph of a function?

Question

Hello

Would someone be kind enough to explain how to "sketch the graph of a function"? The question I have is the following:

y= -8 log₄ x/2

that's -8 log to base4 x over 2

Thank you :)

Answer 1

The following are the usual steps when sketching the graph of a function. By the way, "skething a graph" normally implies NOT working out lots of coordinates for it.

1. Any undefined points. This one is only defined for positive x.

2. What happens near undefined points. When x approaches zero from above this function goes towards positive infinity as the log becomes very negative.

3. Intercepts with axes. No y intercept (see above.) x intercept occurs when y = 0, in this case x = 2 because log(any base) 1 = 0.

4. What happens when x get very large, positive and negative (not in this case). x very large and positive makes function go large and negative.

5. Turning points. Differentiate function and equate to zero.

dy/dx = -8/x cannot be 0 so no turning points. This also shows that gradient starts very negative and continually reduces as x increases. It is -1 when x = 8 so graph is at 45 degrees at this point.

Answer 2

i would just do it the same way i would with any other function: draw up a table of values for 'x' and calculate the corresponding 'y' values (use a calculator). do this to sufficient terms depending on the domain. then, take these sets of points and plot them, before joining them with a smooth curve. remember, as with any log graph, it will have a high gradient to the left, but it will gradually smooth out (in a curve) to being very close to horizontal.