Transforming Exponential Functions

Front

What is the parent function of an exponential function?

Back

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

Front

How does adding a constant to an exponential function affect its graph?

Back

Adding a constant 'k' to the function f(x) = a^x results in a vertical shift of the graph by 'k' units. For example, f(x) = a^x + k shifts the graph up if k > 0 and down if k < 0.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches or crosses. For exponential functions, the horizontal asymptote is typically y = 0.

Front

What does it mean for an exponential function to exhibit growth?

Back

An exponential function exhibits growth when the base 'a' is greater than 1 (e.g., f(x) = 2^x). The graph rises steeply as x increases.

Front

What does it mean for an exponential function to exhibit decay?

Back

An exponential function exhibits decay when the base 'a' is between 0 and 1 (e.g., f(x) = 0.5^x). The graph falls as x increases.

Front

What transformation occurs when the base of an exponential function is negative?

Back

If the base of an exponential function is negative, the function will reflect over the x-axis, resulting in alternating positive and negative values.

Front

What is the effect of multiplying an exponential function by a constant?

Back

Multiplying an exponential function by a constant 'k' (e.g., f(x) = k * a^x) results in a vertical stretch if k > 1 or a vertical compression if 0 < k < 1.

Front

How do you identify the transformation of the function f(x) = 2^(x-3)?

Back

The function f(x) = 2^(x-3) represents a horizontal shift to the right by 3 units from the parent function f(x) = 2^x.

Front

What is the transformation of the function f(x) = 3 * 2^x?

Back

The function f(x) = 3 * 2^x represents a vertical stretch of the parent function f(x) = 2^x by a factor of 3.

Front

What does the term 'vertical translation' refer to in transformations?

Back

Vertical translation refers to shifting the graph of a function up or down without changing its shape.