Functions (Year 12)

Interval Notation

( Excludes the end point (open)

) Excludes the end point (open)

[ Includes the end point (closed)

] Includes the end point (closed)

Inequality

< Less than

≤ Less than or equal to

> Greater than

≥ Greater than or equal to

≠ Not equal to

Vertical Asymptote

The x value that makes denominator = 0

(As long as numerator doesn’t cancel that factor)

Horizontal Asymptote

numerator (n) vs denominator (m)

n < m horizontal asymptote is y = 0

n = m horizontal asymptote is y = a/b

(where a and b are leading coefficients)

n > m no horizontal asymptote

Curve Sketching Menu

1. Domain - Find where the function is defined.

2. Intercepts - Solve x = 0 (y int) and solve y = 0 (x int).

3. Symmetry - If f(-x) = f(x) then even having symmetry about y axis. If f(-x) = -f(x) then odd having symmetry about origin. If neither, then no symmetry.

4. Asymptotes - Steps above.

5. Stationary Points - f’(x) = 0

6. Nature Of Stationary Points - If f’’(x) greater than zero (concave up and min), whereas if less than zero (concave down and max).

7. Points Of Inflection. f’’(x) = 0. Make sure you test.

8. Sketch.