Understanding Exponential Functions

The video introduces exponential functions, explaining their definition and key features such as asymptotes and y-intercepts. It distinguishes between exponential growth and decay, determined by the value of 'b' in the function. The video provides examples to illustrate these concepts and emphasizes the importance of identifying growth or decay and locating the y-intercept and horizontal asymptote.

What is the defining characteristic of an exponential function?

• The variable is in the denominator.

• The variable is an exponent.

• The variable is a constant.

• The variable is a coefficient.

What is an asymptote in the context of exponential functions?

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

• A line that the graph approaches but never touches.

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

• A line that the graph intersects at multiple points.

Where is the y-intercept of an exponential function located?

• At the point (a, 0).

• At the point (b, 0).

• At the point (0, a).

• At the point (0, b).

What determines whether an exponential function represents growth?

• The value of 'a' is greater than 1.

• The value of 'b' is less than 1.

• The value of 'b' is greater than 1.

• The value of 'a' is less than 1.

In exponential decay, what is true about the base 'b'?

• b is less than 1.

• b is equal to 1.

• b is greater than 1.

• b is a negative number.

How can you identify the y-intercept from an equation of an exponential function?

• It is the sum of 'a' and 'b'.

• It is the base 'b'.

• It is the exponent 'x'.

• It is the coefficient 'a'.

In the equation y = 4(1.5)^x, what does the number 4 represent?

• The growth factor.

• The y-intercept.

• The asymptote.

• The decay factor.

For the function y = 5(1/3)^x, what type of function is it?

• Linear function.

• Quadratic function.

• Exponential growth.

• Exponential decay.

What is the horizontal asymptote for the function y = 5(1/3)^x?

• y = x

• y = 5

• y = 0

• y = 1

What will be the focus of the next lessons after learning the characteristics of exponential functions?

• Exploring polynomial functions.

• Studying quadratic functions.

• Graphing and solving exponential functions.

• Solving linear equations.