Exponential Function Transformations

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 the base (a positive real number), and 'x' is the exponent.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is f(x) = b^x, where b > 0 and b ≠ 1.

Front

What does it mean to reflect a function about the x-axis?

Back

Reflecting a function about the x-axis means to invert the output values, changing f(x) to -f(x).

Front

How does translating a function to the right affect its equation?

Back

Translating a function to the right by 'h' units changes the equation from f(x) to f(x - h).

Front

What is the range of the function f(x) = a * b^x when a > 0?

Back

The range is (0, ∞) because the function approaches 0 but never reaches it.

Front

What is the domain of an exponential function?

Back

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

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞.

Front

How do you determine the horizontal asymptote of f(x) = a * b^(x - h) + k?

Back

The horizontal asymptote is y = k.

Front

What transformation occurs when the base of an exponential function is less than 1?

Back

The function is reflected about the x-axis and decreases as x increases.

Front

What does it mean to translate a function vertically?

Back

Translating a function vertically means shifting the graph up or down, changing the equation from f(x) to f(x) + k.