Question

If you were given the equation f ( x ) = 3x⁵+6x, what behavior would the ends of the graph have?

Answer 1

The function given in the problem is a Polynomial Function of degree 5. These functions have the following form: f(x)=ax^5+bx^4+c^3+d^2+ex+f. They have an R domain and their graphs are continuous curves.
 
 You can know the behavior of the function f(x)=3x⁵+6x by given values to the variable x and plot each point obtained. For example:
 
 If x=-1⇒ f(-1)=3(-1)⁵+6(-1)=9
 
 If x=0⇒ f(0)==3(0)⁵+6(0)=0
 
 If x=1⇒ f(1)=3(1)⁵+6(1)=9
 
 Therefore, as you can see in the graph attached, the correct answer is:
 
  c. The left end will start down at a large negative and the right end will go upwards.