When is a function bounded below?

The video tutorial explains the concepts of bounded and unbounded graphs. It starts with the idea of an absolute minimum, where a graph is bounded below, meaning it cannot go lower than a certain point. The tutorial then discusses graphs that are bounded above, using quadratics as an example, where the graph only reaches as high as the vertex, which is an absolute maximum. It contrasts this with unbounded graphs, like cubics, which have no restrictions on how high or low they can go. Finally, it summarizes the concepts of bounded above and below, emphasizing the restrictions on graph behavior.

What does it mean for a graph to be bounded below?

• It can go infinitely high and low.

• It has a minimum point it cannot go below.

• It is restricted to a certain range of x-values.

• It has a maximum height it cannot exceed.

Which type of graph is typically bounded above?

• A sine wave

• A cubic graph

• A linear graph

• A downward-opening quadratic graph

What is the highest point called in a graph that is bounded above?

• The tangent

• The axis

• The vertex

• The minimum

Which of the following graphs is unbounded?

• A quadratic graph

• A cubic graph

• A constant graph

• A linear graph with a slope of zero

What does it mean for a graph to be both bounded above and below?

• It can only decrease indefinitely.

• It is restricted to a certain range of y-values.

• It has no restrictions on its range.

• It can only increase indefinitely.