Question

Which of the following functions could represent the graph below?
f(x) = x(x – a)3(x – b)3
f(x) = (x – a)2(x – b)4
f(x) = x(x – a)6(x – b)2
f(x) = (x – a)5(x – b)

Answer 1

Where's the graph?

Answer 2

http://media.education2020.com/evresources/3111-06-09/mc021-3.jpg

Answer 3

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Answer 4

A good rule of thumb is whether or not the degree of the equation is odd or even. if its even, then both ends go in the same y direction and if its odd they go in opposite y directions. So on your graph, both ends are going in one y direction and so we immediately know its of even degree which allows us to get rid of some options, namely a and c. So we have two options left. What else can we tell about a graph from the equations? Well we can tell how 'flat' it is near the turning critical point from the distribution of powers. From the way the powers are distributed. Because of the way the powers are distributed in d, the graph will drop below the x axis. This leaves the only viable option b.