Graph Functions and Their Characteristics

The video tutorial covers various mathematical functions, including exponential, logarithmic, and circular functions. It explains why circles are not considered functions and introduces the vertical line test to determine if a relation is a function. The tutorial also discusses the effects of switching variables in graphs and explores trigonometric graphs, highlighting the concept of infinite solutions.

What is a key characteristic of exponential functions?

• They have a single y-value for each x-value.

• They have multiple y-values for a single x-value.

• They are always decreasing.

• They have a constant rate of change.

Why are circles not considered functions?

• They do not have a constant rate of change.

• They are not differentiable.

• They are not continuous.

• They have more than one y-value for some x-values.

What does the vertical line test determine?

• If a graph is a function.

• If a graph is differentiable.

• If a graph is linear.

• If a graph is continuous.

What does a vertical line intersecting a graph more than once indicate?

• The graph is not a function.

• The graph is linear.

• The graph is a function.

• The graph is exponential.

What happens when you switch variables in a linear equation?

• It becomes a circular equation.

• It becomes a logarithmic equation.

• It remains a linear equation.

• It becomes a quadratic equation.

How does switching variables affect a parabola?

• It remains unchanged.

• It becomes a circle.

• It becomes a line.

• It turns sideways.

What happens to the graph of y = 2^x when x and y are switched?

• It becomes a linear graph.

• It remains an exponential graph.

• It becomes a circular graph.

• It becomes a logarithmic graph.

What is a limitation of the vertical line test?

• It only works for exponential functions.

• It fails for graphs with infinite intersections.

• It is only applicable to circular graphs.

• It cannot be used for linear functions.

What is the result of switching variables in a trigonometric function?

• The graph remains unchanged.

• The graph turns sideways and fails the vertical line test.

• The graph becomes a circle.

• The graph becomes a straight line.

What is a characteristic of trigonometric functions when variables are switched?

• They become linear functions.

• They pass the vertical line test.

• They have infinite intersections with a vertical line.

• They become exponential functions.