Inequalities and Asymptotes in Graphs

The video tutorial covers solving a polynomial problem by identifying coefficients using the factor theorem. It explains graphing a cubic polynomial and understanding its behavior based on its zeros and leading coefficient. The tutorial also addresses solving inequalities graphically and algebraically, demonstrating the equivalence of different inequalities.

What theorem is used to find the coefficients b, c, and d in the polynomial?

• Pythagorean Theorem

• Factor Theorem

• Remainder Theorem

• Binomial Theorem

What is the factor corresponding to a zero at x = 3?

• x^2 - 9

• x

• x - 3

• x + 3

How does the leading coefficient affect the graph of a polynomial?

• It determines the number of zeros.

• It indicates the direction of the graph as x tends to infinity.

• It changes the degree of the polynomial.

• It affects the width of the graph.

What is the significance of dividing both sides of an inequality by x squared?

• It eliminates the variable x.

• It simplifies the inequality.

• It changes the inequality to an equation.

• It ensures the inequality sign does not change direction.

Why must one be cautious when dividing by x squared in inequalities?

• Because it affects the leading coefficient.

• Because it can introduce complex numbers.

• Because it changes the degree of the polynomial.

• Because x squared can be zero.

What is the result of solving the inequality x^2 - 9 > 0?

• x < -3 or x > 3

• -3 < x < 3

• x = 0

• x > 0

What does the graph of the inequality x^2 - 9/x > 0 look like?

• A graph with vertical and oblique asymptotes

• A circle

• A line with a positive slope

• A parabola opening upwards

What is the vertical asymptote of the graph of the inequality x^2 - 9/x > 0?

• x = 9

• x = 0

• x = 3

• x = -3

What is the oblique asymptote of the graph of the inequality x^2 - 9/x > 0?

• y = x

• y = 0

• y = x^2

• y = -x

How are the inequalities x^2 - 9 > 0 and x^2 - 9/x > 0 related?

• One is a subset of the other.

• They have no relation.

• They are equivalent.

• They have different solutions.