Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for an exponential function to decay?

Back

Decay in an exponential function occurs when the base 'b' is between 0 and 1, resulting in a decrease in the value of the function as 'x' increases.

Front

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

Back

The range is y > 0, meaning the function outputs positive values only.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a * b^x is the value of 'y' when 'x' = 0, which is equal to 'a'.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

How does the graph of an exponential function behave as x approaches infinity?

Back

As x approaches infinity, the graph of an exponential function with a base greater than 1 increases without bound, while a base between 0 and 1 approaches 0.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is f(x) = b^x, where b is a positive real number.

Front

What effect does translating an exponential function horizontally have on its equation?

Back

Translating an exponential function horizontally involves adjusting the exponent, resulting in an equation of the form g(x) = b^(x - h) for a translation of h units.

Front

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

Back

The base 'b' determines the growth or decay rate of the function; if b > 1, the function grows, and if 0 < b < 1, the function decays.

Front

How do you identify the vertical asymptote of an exponential function?

Back

The vertical asymptote of an exponential function is typically the line y = 0, which the graph approaches but never touches.