1. Guidelines for sketching the graph of a function
4.5 Graphical Methods.
Guidelines for sketching the graph of a function
using first and second derivative.
Rita Korsunsky

2. Guidelines for sketching the graph of y = f(x)
There are seven guidelines to follow while sketching a graph.
1. Domain – find all x that are possible.
The denominator of a function cannot equal 0.
2. Continuity – determine whether f is continuous on its domain.
f is a rational function, it is continuous on its domain,
but f has infinite discontinuities at –3 and 3 which are not on the domain
The domain of f consists of all
real numbers except –3 and 3.

3. 3. Intercepts – find the x-and y-intercepts.
The graph intersects both axes at the origin.

4. 4. Symmetry – check to see if the function is odd or even.
If the function is even, the graph will be symmetrical with respect to the y-axis.
If the function is odd, the graph will be symmetrical with respect to the origin.
Ex:

5. -3 3 f

6. 6 a. Points of Inflection
6 b. Concavity
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+ + -3 3
f’’
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7. 7. Asymptotes: lines graph is approaching to.
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Horizontal asymptote : y = -2

8. + +

9. Check using graphing calculator:
Time to graph!
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Check using graphing calculator:

10. Continuous on its domain, But it has infinite discontinuity at x=2
4.Symmetry:
2.Continuity
Continuous on its domain,
But it has infinite discontinuity at x=2
3.Intercepts:
x-intercepts: y =0
y-intercepts: x =0

11. + - 6.Points of Inflection and Concavity:
5.Critical Numbers and Extrema:
+ + 2
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12. 6.Asymptotes:
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13. Check using graphing calculator:
Time to graph!
Check using graphing calculator:
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