Transformations and Inverse Functions

Front

What is a transformation in mathematics?

Back

A transformation is an operation that moves or changes a shape or function in some way, such as translation, rotation, reflection, or dilation.

Front

What does the notation g(x) = f(x - 1) - 5 represent?

Back

This notation represents a transformation of the function f(x) where the graph is translated to the right by 1 unit and down by 5 units.

Front

How does the function f(x + k) affect the graph of f(x)?

Back

The function f(x + k) shifts the graph of f(x) to the left by k units.

Front

What effect does the equation g(x) = f(x) - 4 have on the graph of f(x)?

Back

The equation g(x) = f(x) - 4 shifts the graph of f(x) down by 4 units.

Front

What is the parent function of g(x) = x^2?

Back

The parent function is the simplest form of a function, which in this case is f(x) = x^2, representing a basic quadratic function.

Front

If g(x) = f(x) + k, what does this do to the graph of f(x)?

Back

The equation g(x) = f(x) + k shifts the graph of f(x) upwards by k units.

Front

What does the transformation g(x) = f(x + 3) do to the graph of f(x)?

Back

The transformation g(x) = f(x + 3) shifts the graph of f(x) to the left by 3 units.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph across the x-axis.

Front

What does the transformation g(x) = 2f(x) do to the graph of f(x)?

Back

The transformation g(x) = 2f(x) vertically stretches the graph of f(x) by a factor of 2.

Front

What is the result of the transformation g(x) = f(x - 2) + 1?

Back

The transformation g(x) = f(x - 2) + 1 shifts the graph of f(x) to the right by 2 units and up by 1 unit.