Graph Transformations!

Front

What is a graph transformation?

Back

A graph transformation is a change made to the graph of a function that alters its position, shape, or orientation on the coordinate plane.

Front

What does the transformation y = f(-x) represent?

Back

This transformation reflects the graph of f(x) across the y-axis.

Front

What does the transformation y = -f(x) represent?

Back

This transformation reflects the graph of f(x) across the x-axis.

Front

What does the transformation y = f(x + c) represent?

Back

This transformation shifts the graph of f(x) horizontally to the left by c units.

Front

What does the transformation y = f(x - c) represent?

Back

This transformation shifts the graph of f(x) horizontally to the right by c units.

Front

What does the transformation y = f(x) + c represent?

Back

This transformation shifts the graph of f(x) vertically upwards by c units.

Front

What does the transformation y = f(x) - c represent?

Back

This transformation shifts the graph of f(x) vertically downwards by c units.

Front

If f(x) is a quadratic function, what is the effect of y = -f(x)?

Back

The graph of the quadratic function is reflected over the x-axis, resulting in a downward-opening parabola.

Front

How does the graph of y = f(x + 2) differ from y = f(x)?

Back

The graph of y = f(x + 2) is shifted 2 units to the left compared to y = f(x).

Front

How does the graph of y = f(x) - 5 differ from y = f(x)?

Back

The graph of y = f(x) - 5 is shifted 5 units downward compared to y = f(x).