transformation of exponential function

Front

What is a transformation in the context of exponential functions?

Back

A transformation refers to a change in the position, size, or shape of the graph of an exponential function, which can include translations, reflections, stretches, and compressions.

Front

What does a vertical translation of an exponential function do?

Back

A vertical translation shifts the graph of the function up or down without changing its shape.

Front

What does a horizontal translation of an exponential function do?

Back

A horizontal translation shifts the graph of the function left or right without changing its shape.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, represented as (0, ∞).

Front

What is a horizontal asymptote?

Back

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

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Back

Front

How does a vertical compression affect the graph of an exponential function?

Back

A vertical compression reduces the height of the graph, making it flatter, while keeping the horizontal asymptote unchanged.

Front

What does a vertical shift of an exponential function do?

Back

A vertical shift moves the graph up or down by adding or subtracting a constant from the function.

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.