Exponential Functions

Front

What is an exponential function?

Back

An exponential function is 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.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is a horizontal line that the graph approaches as x approaches positive or negative infinity.

Front

What is the vertical asymptote of an exponential function?

Back

Exponential functions do not have vertical asymptotes; they can extend infinitely in the vertical direction.

Front

How does the graph of f(x) = b^x change when 'b' is greater than 1?

Back

When 'b' is greater than 1, the graph of f(x) = b^x shows exponential growth.

Front

How does the graph of f(x) = b^x change when 'b' is between 0 and 1?

Back

When 'b' is between 0 and 1, the graph of f(x) = b^x shows exponential decay.

Front

What is the effect of adding a constant to an exponential function, such as f(x) = b^x + k?

Back

Adding a constant 'k' shifts the graph vertically by 'k' units. If k is positive, the graph shifts up; if negative, it shifts down.

Front

What is the effect of subtracting a constant from an exponential function, such as f(x) = b^x - k?

Back

Subtracting a constant 'k' shifts the graph vertically down by 'k' units.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than zero, (0, ∞).