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Power Functions (part 1). Power functions: A) Is any function whose first term is x n where “n” is any number ( pos , neg , fraction, decimal, etc.). 1) The exponent is called the power (or degree). B) A power function can have more than one term.
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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 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 3x2) 1) This coefficient is a constant value so it is also called the constant of variation.
Power Functions (part 1) II. Transformation the coefficient created 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.
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 know as a parent function (has no transformations).
