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# Power Functions

## 3.5 Transformations of Polynomial Functions

#### Transformations with Power Functions

• Recall that power functions has the form y=x^n, where is a real number. We have looked into cases where is a rational number, which includes positive and negative whole numbers and fractions.
• Transformation can be applied on power functions. The transformed equation simply take the general form of f(x)=a(b(x-c))^{n}+d, where a,\ b,\ c,\ d are real numbers.

i) If it is a reflection, we have b=-1 or a=-1.

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## 1.2 Power Functions

#### Introduction to Power Functions

• Power functions are functions with the form f(x)=x^{n}, where n is a rational number.
• Some examples of power functions are:

f(x)=x^{2},\ f(x)=x^{4},\ f(x)=x^{\frac{1}{4}},\ f(x)=x^{-5},\ f(x)=x^{\frac{1}{3}}

• The expression x^n is read as: ‘x to the power of n’.

#### Drawing Power Functions (for Positive Integers) and its Graph Properties

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