12.18.23 PAP A2 Transformations with a Point/Graph

Front

What is a transformation in mathematics?

Back

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

Front

What does the notation g(x) = f(x + c) represent?

Back

This represents a horizontal translation of the function f(x) to the left by c units.

Front

What does the notation g(x) = f(x) + k represent?

Back

This represents a vertical translation of the function f(x) upward by k units.

Front

What is the effect of multiplying a function by a factor greater than 1?

Back

It vertically stretches the graph of the function.

Front

What is the effect of multiplying a function by a factor between 0 and 1?

Back

It vertically compresses the graph of the function.

Front

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

Back

This represents a reflection of the graph of f(x) across the x-axis.

Front

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

Back

This represents a reflection of the graph of f(x) across the y-axis.

Front

How does the point (-4, 5) change when transformed by g(x) = f(x + 2)?

Back

The point moves to (-6, 5) due to a horizontal translation left by 2 units.

Front

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

Back

The parent function is f(x) = |x|, which is the absolute value function.

Front

What is the effect of adding a constant to the function inside the absolute value?

Back

It shifts the graph horizontally.