Understanding Exponential and Cubic Functions

The video tutorial covers famous mathematical curves, including cubic, reciprocal, and exponential functions. It explains the characteristics and graph behaviors of each function, focusing on how the sign of constants affects the graph's shape and direction. The tutorial emphasizes the importance of visualizing these graphs to understand their properties better.

What is the basic form of a quadratic function?

• y = ax + b

• y = ax^2 + bx + c

• y = ax^3 + bx^2 + cx + d

• y = a/x

How does the sign of 'a' affect the shape of a cubic function's graph?

• It affects the steepness of the graph.

• It decides the direction of the graph's ends.

• It has no effect on the graph.

• It determines the y-intercept.

What does the graph of a cubic function look like when 'a' is negative?

• It opens upwards.

• It forms a straight line.

• It opens downwards.

• It becomes a circle.

What is the general shape of the graph of a cubic function?

• A straight line

• A parabola

• An S-shaped curve

• A circle

What is the effect of a negative 'a' in the cubic function?

• The graph opens upwards.

• The graph forms a circle.

• The graph opens downwards.

• The graph becomes a straight line.

What happens to the graph of y = a/x when 'a' is positive?

• It approaches the y-axis but never touches it.

• It forms a parabola.

• It becomes a straight line.

• It intersects the x-axis.

In the reciprocal function y = a/x, what occurs when 'a' is negative?

• The graph flips across the y-axis.

• The graph remains unchanged.

• The graph becomes a horizontal line.

• The graph flips across the x-axis.

In the context of the reciprocal function, what does it mean for the graph to be 'disjoint'?

• The graph is a single continuous curve.

• The graph consists of two separate branches.

• The graph intersects the x-axis.

• The graph forms a closed loop.

How does the graph of y = a/x behave as it approaches the x-axis?

• It gets closer but never touches the x-axis.

• It moves away from the x-axis.

• It forms a loop.

• It intersects the x-axis.

What is a key feature of the graph of y = a/x when 'a' is positive?

• It approaches but never touches the axes.

• It forms a closed loop.

• It is a straight line.

• It intersects the y-axis.