Quick guide to sketching curves (1 Viewer)

[housemouse]

I have serious problems sketching curves because i have no idea what to do.

Could someone suggest a short guide to sketching curves of all sorts.

 

[Riviet]

These are some techniques that I use (sought of in the order shown) to sketch any curve:

• domain
• x and y intercepts
• horizontal and vertical asymptotes
• As x->infinity, y->?
• guide graph(s) are very useful
• plot points to see if curve is above or below x-axis
• find any stationary points or points of inflexion and check their nature

 

[acullen]

Here's a really brief summary:

Point of Inflexion
Occurs where f"(x)=0
A point of inflexion is a point where concavity changes in the function.

Stationary Point
Any point where f'(x)=0
A point in the function where the gradient is equal to 0.

Maxima/Minima
A special case where f'(x)=0
A stationary point of a function that yields either the greatest or lowest value for y
Possibly the easiest way to determine a stationary point is to test the gradient (ie first derivative) just before and just after the line. A maxima will have a positive gradient just before it and a negative gradient just afterwards (assuming a continuous function). Conversely, the opposite is true for a minima.

Other Notes
Always inspect the function carefully, there will be instances where you are given a function that is non-continuous.
e.g. f(x)=sin^-1(x)
Dom(x)={-1 ≤ 0 ≤ 1}
.'. The f(x) is undefined for all values < -1, > 1. This means you obviously will end the graph line at those points.

 

[joesmith1975]

but sketching curves course in the 4unit requires no calculus.

 

[haboozin]

but sketching curves course in the 4unit requires no calculus.

dont be so sure

i think it was 1992 hsc