Transformations of Exponential Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, which can include shifts, stretches, compressions, and reflections.

Front

What does a vertical shift of a function do?

Back

A vertical shift moves the graph of the function up or down without changing its shape.

Front

What effect does adding a constant to the function have?

Back

Adding a constant to the function shifts the graph vertically. For example, if f(x) is transformed to f(x) + 3, the graph shifts up by 3 units.

Front

What does the equation g(x) = f(x - 3) represent?

Back

The equation g(x) = f(x - 3) represents a horizontal shift of the graph of f(x) to the right by 3 units.

Front

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

Back

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

Front

How does a coefficient greater than 1 affect the graph of a function?

Back

A coefficient greater than 1 vertically stretches the graph of the function.

Front

What does a coefficient between 0 and 1 do to the graph?

Back

A coefficient between 0 and 1 vertically compresses the graph of the function.

Front

What is the parent function of a quadratic equation?

Back

Front

What transformation does the equation y = -2(x + 1)^2 + 3 indicate?

Back

The equation indicates a reflection across the x-axis, a vertical stretch by a factor of 2, and a shift 3 units up.

Front

What does the term 'horizontal compression' mean?

Back

Horizontal compression occurs when the graph of a function is squeezed towards the y-axis, typically caused by a coefficient greater than 1 in the x-term.