Exponential Functions Concepts and Properties

The video tutorial covers the basics of exponential functions, including their definition, properties, and examples. It explains how to plot exponential graphs and discusses their characteristics, such as asymptotes. The tutorial also covers transformations like reflections and translations, and provides detailed steps and examples for sketching exponential graphs. Advanced techniques for understanding and sketching these graphs are also discussed.

What distinguishes an exponential function from a polynomial function?

• The variable is in the base.

• The function is always quadratic.

• The variable is in the exponent.

• The function is always linear.

Which of the following is a condition for a function to be exponential?

• The base must be a negative real number.

• The base must be a positive real number other than 1.

• The base can be any real number.

• The base can be zero.

What happens to the graph of an exponential function as the base increases?

• It oscillates more.

• It becomes more linear.

• It becomes steeper and moves away from the x-axis more quickly.

• It becomes flatter and closer to the x-axis.

What is an asymptote in the context of exponential functions?

• A line that the graph never touches.

• A point where the graph intersects the x-axis.

• A line that the graph crosses multiple times.

• A point where the graph intersects the y-axis.

How does reflecting an exponential function in the y-axis affect its graph?

• It shifts the graph upwards.

• It mirrors the graph over the x-axis.

• It shifts the graph downwards.

• It mirrors the graph over the y-axis.

What is the effect of a dilation on an exponential function?

• It changes the base of the function.

• It changes the direction of the graph.

• It stretches or compresses the graph vertically.

• It shifts the graph horizontally.

When sketching an exponential graph, what is important to calculate?

• Only the asymptote.

• Both x and y intercepts, and any other relevant points.

• Only the y-intercept.

• Only the x-intercept.