classify each function as a power function, root function.......

Question

classify each function as a power function, root function, polynomial (state in degrees), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. 

1. y = π^x (pi to the x power) 

2. y = x^π (x to the pi power) 

3. y = x^2 (2-x^3)

4. y = tan t - cos t

5. y = s/ 1+s

6. y = (sqrt(x^3)-1) / 1 + (the cubed root of x)

 

first day of class need a refresher! 

Answer 1

1)

 

This is constant raised to the x power.  This is exponential.

 

 

2)

 

This is variable raised to a constant.  Therefore, a power function.

 

 

3)

 

A polynomial of degree 5.

 

 

4)

 

This one is obvious.

 

 

5)

 

Anything in fraction form is rational.

 

 

6)

 

y = [- 1 + √(x³)] / [1 + ³√(x)]

 

y = [- 1 + x√x)] / [1 + ³√(x)]

 

 

The domain in this function is all real numbers in the interval [0, ∞).  It is a root function.