Exponential Functions Transformation [24-25]

Front

What is the parent function of exponential functions?

Back

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

Front

What does it mean to translate an exponential function vertically?

Back

Translating an exponential function vertically means adding or subtracting a constant to/from the function, which shifts the graph up or down.

Front

What is the effect of a positive constant added to an exponential function?

Back

Adding a positive constant to an exponential function shifts the graph upward.

Front

What is the effect of a negative constant subtracted from an exponential function?

Back

Subtracting a negative constant from an exponential function shifts the graph downward.

Front

How does changing the base of an exponential function affect its graph?

Back

Changing the base affects the growth rate of the function; larger bases grow faster.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^(x - h) + k, where (h, k) is the translation.

Front

What is the significance of the horizontal asymptote in an exponential function?

Back

The horizontal asymptote represents the value that the function approaches as x approaches infinity or negative infinity.

Front

How do you identify the parent function from a transformed exponential function?

Back

The parent function can be identified by removing any translations or transformations applied to the function.

Front

What does the notation f(x) = 3^(x-2) + 1 represent?

Back

This represents an exponential function that has been translated 2 units to the right and 1 unit up from its parent function f(x) = 3^x.

Front

What is the effect of a negative coefficient in front of an exponential function?

Back

A negative coefficient reflects the graph across the x-axis.