Exponential Functions Key features

What is the general form of an exponential function?

• f(x) = a * b^x, where 'a' is a constant and 'b' is the base

• f(x) = a + b^x, where 'a' is a constant and 'b' is the base

• f(x) = a - b^x, where 'a' is a constant and 'b' is the base

• f(x) = a / b^x, where 'a' is a constant and 'b' is the base

What does the base 'b' in an exponential function indicate?

• The base 'b' indicates the growth (b > 1) or decay (0 < b < 1) rate of the function.

• The base 'b' determines the maximum value of the function.

• The base 'b' represents the horizontal shift of the function.

• The base 'b' indicates the vertical stretch of the function.

How can you determine if an exponential function is increasing or decreasing?

• If the base 'b' is greater than 1, the function is increasing; if 0 < b < 1, the function is decreasing.

• If the base 'b' is equal to 1, the function is constant.

• If the base 'b' is less than 0, the function is decreasing.

• If the base 'b' is greater than 2, the function is always increasing.

What is the formula for the horizontal asymptote of an exponential function?

• y = 0

• y = 1

• y = x

• y = -1

What is the y-intercept of the function f(x) = 3 * 2^x?

• 1

• 2

• 3

• 4

What is the effect of changing the base 'b' in an exponential function?

• It has no effect on the function.

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

• It changes the function to a linear function.

• It only affects the y-intercept of the function.

What is the range of an exponential function of the form f(x) = a * b^x where a > 0?

• y > 0

• y < 0

• y = 0

• y is any real number

What is the horizontal asymptote of an exponential function?

• y = 0

• y = 1

• y = -1

• y = x

What happens to the value of f(x) as x approaches infinity in an exponential decay function?

• f(x) approaches infinity

• f(x) approaches a constant value

• f(x) approaches the horizontal asymptote, which is typically y = 0

• f(x) oscillates between two values

What is the relationship between the y-intercept and the initial value in an exponential function?

• The y-intercept is equal to the initial value of the function when x = 0.

• The y-intercept is always greater than the initial value.

• The y-intercept is the same as the maximum value of the function.

• The y-intercept has no relation to the initial value.