Graphing Exponential Functions

What is the significance of the y-intercept in exponential functions?

• It represents the maximum value of the function.

• It indicates the rate of growth or decay of the function.

• It represents the initial value of the function at x = 0, indicating the starting point of the exponential growth or decay.

• It shows the asymptotic behavior of the function as x approaches infinity.

How do you determine if a function is exponential growth or decay?

• If the base of the exponential function is greater than 1, it is exponential growth; if the base is between 0 and 1, it is exponential decay.

• If the base of the exponential function is equal to 1, it is neither growth nor decay.

• If the base of the exponential function is negative, it is exponential decay.

• If the base of the exponential function is greater than 0, it is exponential growth.

What is an exponential function?

• A mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

• A function that grows linearly over time.

• A function that has a constant rate of change.

• A function that can only take positive values.

What happens to the graph of an exponential function as x approaches infinity?

• The graph of an exponential growth function rises indefinitely, while an exponential decay function approaches the horizontal asymptote.

• The graph of both exponential growth and decay functions remains constant.

• The graph of an exponential growth function falls indefinitely, while an exponential decay function rises indefinitely.

• The graph of both exponential growth and decay functions oscillates between two values.

What is the initial value in the function f(x) = 13(0.27)^x?

• 10

• 13

• 15

• 20

What is exponential growth?

• A process where a quantity increases by a consistent percentage over time, represented by f(x) = a * b^x where b > 1.

• A linear increase in quantity over time, represented by f(x) = a + bx.

• A decrease in quantity over time, represented by f(x) = a * e^(-bx).

• A random fluctuation in quantity without a defined pattern.

How can you identify exponential functions from a set of equations?

• Exponential functions can be identified by their form f(x) = a * b^x, where 'b' is a constant base raised to the power of 'x'.

• Exponential functions are characterized by a linear form f(x) = mx + b.

• Exponential functions can be identified by their form f(x) = a + b * x^2, where 'b' is a constant coefficient.

• Exponential functions are defined as f(x) = a * e^x, where 'e' is the base of natural logarithms.

What does the base of an exponential function indicate?

• It indicates the function's domain.

• It indicates the growth or decay rate; if the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay.

• It determines the function's intercepts.

• It specifies the maximum value of the function.

What is the horizontal asymptote of f(x) = 2(3^x)?

• y = 0

• y = 2

• y = 3

• y = -2

How do you find the y-intercept of f(x) = 3^x?

• (0, 1)

• (0, 3)

• (1, 0)

• (3, 0)