Graphing Polynomial Functions — Quiz

Question 8 • Mathematics III

Which graph shows the same end behavior as the graph of f of x is equal to 2 x to the 6th power minus 2 x squared minus 5 ?

Answer

Image with description On a coordinate plane, a polynomial graph is drawn. It starts from quadrant 2, moves down and crosses negative x axis 2 units from the origin, moves up and crosses the positive y axis 2 point 5 units from the origin, it moves to quadrant 4, curves down and passes through positive x axis, 2 units from the origin, and passes through quadrant 4.

Image with description On a coordinate plane a polynomial graph is drawn. The graph starts from quadrant 3, touches the x axis 5 units left of the origin, moves down, crosses the y axis 5 units below the origin, curves up and passes through the x axis 4 units to the right of the origin, and move through quadrant 1.

Image with description On a coordinate plane a polynomial graph is drawn. It starts from quadrant 2, moves down, touches the negative x axis, 2 units from the origin, curves up and passes through the positive y axis. It curves down and touches positive x axis two units from the origin and moves through quadrant 1.

Image with description On a coordinate plane a polynomial graph is drawn. It starts from quadrant 3, moves up and touches the negative x axis 5 units from the origin, curves down and passes through negative y axis, curves up, touches the positive x axis 5 units from the origin and curves down and passes through quadrant 4.

Explanation

The leading term is 2x⁶, and it determines the polynomial’s end behavior. Since the degree is even and the leading coefficient is positive, the graph rises on both ends: it goes up to the left in quadrant 2 and up to the right in quadrant 1. Choice B has that end behavior.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz