Understanding Exponential Functions

The video tutorial reviews the characteristics of exponential functions, including their general form, x-intercept, y-intercept, asymptote, end behavior, and how to determine if they are increasing or decreasing. It also covers the domain and range of these functions and analyzes a second function with different parameters.

What is the general form of an exponential function?

• y = mx + b

• y = ax^2 + bx + c

• y = a * b^x

• y = a/x

What is the x-intercept of an exponential function with an asymptote at y = 0?

• There is no x-intercept

• x = 0

• x = 1

• x = -1

How is the y-intercept of an exponential function determined?

• By finding the slope

• By setting x = 0

• By setting y = 0

• By calculating the derivative

What is the end behavior of exponential functions?

• They approach the y-axis

• They remain constant

• They oscillate

• They move between quadrant two and quadrant one

What determines if an exponential function is increasing or decreasing?

• The value of the base

• The value of the exponent

• The value of the constant term

• The value of the coefficient

If the base of an exponential function is between 0 and 1, what is the nature of the function?

• Increasing

• Decreasing

• Constant

• Oscillating

What is the equation of the asymptote for the exponential functions discussed?

• y = 1

• y = -1

• y = 0

• y = x

What is the domain of the exponential functions discussed?

• x is positive

• x is negative

• x is integer

• x is real

What is the range of the exponential functions discussed?

• y > 0

• y < 0

• y = 0

• y is any real number

For the second function, what is the y-intercept if the a value is 0.5?

• 0

• 0.5

• 1

• 2