Precalculus Polynomial Functions and Their Graphs Quiz: 10 Questions with Explanations

A 3B 4C 5D 2

The degree is the highest exponent, 5, even though it is not written first.

A Left down, right upB Both ends upC Both ends downD Left up, right down

Odd degree with a negative leading coefficient: left up, right down.

A Crosses the x-axisB Touches the x-axis and turnsC Has a vertical asymptoteD Never reaches the x-axis

Even multiplicity bounces off the axis.

A \(-2\) and \(5\)B \(2\) and \(-5\)C \(2\) and \(5\)D \(-2\) and \(-5\)

Set each factor to zero: x = 2 and x = -5. The sign flips when moving the constant across.

A 4B 3C 2D 5

It crosses at -2 and 3 and touches at 1 (multiplicity 2): 1 + 2 + 1 = 4.

A 5B 3C 6D 4

A polynomial of degree n has at most n – 1 turning points.

A \(6\)B \(-1\)C \(-6\)D \(5\)

f(0) = (2)(-3) = -6. Using the zeros instead gives the x-intercepts.

A Ends point opposite directionsB Both ends point the same directionC The graph is a lineD It has no turning point

Even-degree polynomials have ends that both go up or both go down.

A \((-4,1)\)B \((-\infty,-4)\cup(1,\infty)\)C \([-4,1]\)D \((-1,4)\)

The product is negative between the zeros -4 and 1. The endpoints are excluded for a strict inequality.

A \((x+1)(x-2)(x-3)\)B \(-(x+1)(x-2)(x-3)\)C \((x-1)(x+2)(x+3)\)D \((x+1)(x-2)^{2}(x-3)\)

Each zero gives a factor (x – r), and a positive leading coefficient with odd degree rises on the right.