Identifying Transformations

Front

What is a transformation in the context of graphing functions?

Back

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

Front

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

Back

It shifts the graph of f(x) to the right by c units if c is positive, and to the left by c units if c is negative.

Front

What is the effect of the transformation g(x) = f(x) + k on the graph of f(x)?

Back

It shifts the graph of f(x) up by k units if k is positive, and down by k units if k is negative.

Front

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

Back

It multiplies the output of the function by a, making the graph taller and steeper.

Front

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

Back

It multiplies the output of the function by a, making the graph shorter and less steep.

Front

How does the transformation g(x) = -f(x) affect the graph of f(x)?

Back

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

Front

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

Back

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

Front

If f(x) = x^2, what is the transformation for g(x) = (x + 3)^2?

Back

The graph of f(x) shifts 3 units to the left.

Front

If f(x) = 2^x, what is the transformation for g(x) = 2^{x - 1}?

Back

The graph of f(x) shifts 1 unit to the right.

Front

What is the parent function for quadratic equations?

Back

The parent function for quadratic equations is f(x) = x^2.