1. Power Functions (part 1)
Steven Kudolis
Power Functions (part 1)
Power functions:
A) Is any function whose first term is xn where “n” is any
number (pos, neg, fraction, decimal, etc.).
1) The exponent is called the power (or degree).
B) A (non-power) function can have more than one term.
1) Standard form has them written in order from
the biggest exponent (the degree of the function),
then next biggest, and so on. (ex: 3x2 + 5x – 8)
C) A power function can have a constant (a coefficient) in
front of the variable. (The 3 in y = 3x2 )
1) This coefficient is a constant value so it is also
called the constant of variation.
D) The power function y = Axn is symmetrical.

2. Power Functions (part 1)
Steven Kudolis
Power Functions (part 1)
II. Transformations the coefficient creates in f(x) = Axn
A) The constant of variation causes a transformation similar
to the one the “m” term in y = mx + b causes.
1) If the |value| of “A” is bigger than one, it gets taller
faster than it gets wide. This is a Vertical Stretch.
2) If the |value| of “A” is less than one, it gets wider faster
than it gets tall, so it is shorter. A Vertical Shrink.
3) If the value of “A” is negative, it still follows the same
rules as above excepts it also flips upside-down.
a) A reflection across the x-axis.

3. Power Functions (part 1)
Steven Kudolis
Power Functions (part 1)
B) Shift rules for f(x) = A●xn
1) If | A | > 1, then it is taller (vertical stretch).
2) If | A | < 1, then it is shorter (vertical shrink).
3) If A is negative, then the graph flips upside-down.
(reflects over the x-axis)
a) And is still taller or shorter based on if the absolute value
of A is more or less than one.
4) If A = +1, then no change occurs to f(x) = xn
a) This is known as a parent function (has no transformations).

4. Power Functions (part 1)
Steven Kudolis
Power Functions (part 1)

5. Power Functions (part 1)
Steven Kudolis
Power Functions (part 1)