6.6 Transformations of Exponential Functions

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where 'a' is a constant, 'b' is the base (b > 0, b ≠ 1), and 'x' is the exponent.

Front

What does a positive value of 'a' indicate in an exponential function?

Back

A positive value of 'a' indicates that the function will grow exponentially as x increases.

Front

What does a negative value of 'a' indicate in an exponential function?

Back

A negative value of 'a' indicates that the function will decrease exponentially as x increases.

Front

How does the base 'b' affect the growth of an exponential function?

Back

If b > 1, the function grows; if 0 < b < 1, the function decays.

Front

What is a transformation of a function?

Back

A transformation of a function is a change made to the function's graph, which can include shifts, stretches, compressions, or reflections.

Front

What does a horizontal shift to the right by 'h' units look like in an exponential function?

Back

The transformation is represented as f(x) = a * b^(x - h).

Front

What does a vertical shift upward by 'k' units look like in an exponential function?

Back

The transformation is represented as f(x) = a * b^x + k.

Front

What is the effect of a vertical compression on an exponential function?

Back

A vertical compression by a factor of 'c' (0 < c < 1) is represented as f(x) = c * a * b^x.

Front

What is the effect of a vertical stretch on an exponential function?

Back

A vertical stretch by a factor of 'c' (c > 1) is represented as f(x) = c * a * b^x.

Front

How do you represent a reflection over the x-axis in an exponential function?

Back

A reflection over the x-axis is represented as f(x) = -a * b^x.