The document discusses how to sketch the graph of a reciprocal function y = 1/f(x). Key steps include:
1) Drawing the original function y = f(x) first,
2) Noting that vertical asymptotes occur where f(x) = 0,
3) Asymptotes become x-intercepts as f(x) approaches infinity,
4) The reciprocal function is decreasing where the original is increasing and vice versa.
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
X2 t07 04 reciprocal functions (2012)
1. (G) Graphs of Reciprocal
1
Functions
The graph of y can be sketched by first drawing y f x
f x
and noticing;
2. (G) Graphs of Reciprocal
1
Functions
The graph of y can be sketched by first drawing y f x
f x
and noticing;
1
when f x 0, then is undefined, i.e. a vertical asymptote exists
f x
5. (G) Graphs of Reciprocal
1
Functions
The graph of y can be sketched by first drawing y f x
f x
and noticing;
1
when f x 0, then is undefined, i.e. a vertical asymptote exists
f x
1
when f x , then 0, i.e. asymptotes become x intercepts
f x
10. (G) Graphs of Reciprocal
1
Functions
The graph of y can be sketched by first drawing y f x
f x
and noticing;
1
when f x 0, then is undefined, i.e. a vertical asymptote exists
f x
1
when f x , then 0, i.e. asymptotes become x intercepts
f x
when f x is increasing, the reciprocal is decreasing, and visa - versa
11. (G) Graphs of Reciprocal
1
Functions
The graph of y can be sketched by first drawing y f x
f x
and noticing;
1
when f x 0, then is undefined, i.e. a vertical asymptote exists
f x
1
when f x , then 0, i.e. asymptotes become x intercepts
f x
when f x is increasing, the reciprocal is decreasing, and visa - versa
1
when f x is positive, is positive, etc.
f x
13. (G) Graphs of Reciprocal
1
Functions
The graph of y can be sketched by first drawing y f x
f x
and noticing;
1
when f x 0, then is undefined, i.e. a vertical asymptote exists
f x
1
when f x , then 0, i.e. asymptotes become x intercepts
f x
when f x is increasing, the reciprocal is decreasing, and visa - versa
1
when f x is positive, is positive, etc.
f x
1 -f x
the derivative of is , hence stationary points of the
f x f x 2
original curve are stationary points of its reciprocal.