Function Transformations

Front

What is the effect of the transformation g(x) = f(x) - 1 on the graph of f(x)?

Back

The graph of f(x) is shifted down by 1 unit.

Front

How do you describe the transformation of a function that is reflected over the y-axis, vertically stretched by a scale factor of 5, and shifted 4 units down?

Back

The transformation can be described by the rule g(x) = 5f(-x) - 4.

Front

If g(x) = f(x) - 5, what transformation has occurred compared to f(x)?

Back

The graph of f(x) is shifted down by 5 units.

Front

What transformations are applied to f(x) to obtain g(x) = -1/2 f(x - 4) + 1?

Back

The graph is reflected across the x-axis, compressed by a factor of 1/2, shifted 4 units to the right, and shifted 1 unit up.

Front

What does the transformation g(x) = f(x) + 4 do to the graph of f(x)?

Back

The graph of f(x) is shifted up by 4 units.

Front

What is the general effect of a negative sign in front of a function, such as g(x) = -f(x)?

Back

The graph of f(x) is reflected across the x-axis.

Front

What does a vertical stretch by a factor of k do to the graph of a function f(x)?

Back

The graph is stretched away from the x-axis by a factor of k.

Front

How does shifting a function to the right affect its equation?

Back

To shift a function f(x) to the right by h units, replace x with (x - h) in the function's equation.

Front

What is the effect of a horizontal compression by a factor of k on the function f(x)?

Back

The graph is compressed towards the y-axis by a factor of k.

Front

What transformation occurs when you replace f(x) with f(-x)?

Back

The graph of f(x) is reflected over the y-axis.