Transformations in Function Notation

Front

What is a reflection over the x-axis in function notation?

Back

If g(x) = -f(x), the graph of f is reflected over the x-axis.

Front

What does a vertical translation up by 6 units look like in function notation?

Back

If g(x) = f(x) + 6, the graph of f is shifted vertically up by 6 units.

Front

How does a horizontal shrink by a factor of 1/5 appear in function notation?

Back

If g(x) = f(5x), the graph of f is horizontally shrunk by a factor of 1/5.

Front

What is the effect of a horizontal translation left by 5 units in function notation?

Back

If g(x) = f(x + 5), the graph of f is shifted horizontally left by 5 units.

Front

What does the transformation g(x) = 2f(x - 6) + 15 represent?

Back

It represents a horizontal translation right by 6, a vertical stretch by 2, and a vertical translation up by 15.

Front

What is the general form for a vertical stretch by a factor of k?

Back

If g(x) = kf(x), where k > 1, the graph of f is vertically stretched by a factor of k.

Front

What does a horizontal stretch by a factor of k look like in function notation?

Back

If g(x) = f(x/k), where k > 1, the graph of f is horizontally stretched by a factor of k.

Front

How do you denote a vertical translation down by c units?

Back

If g(x) = f(x) - c, the graph of f is shifted vertically down by c units.

Front

What is the transformation for a reflection over the y-axis?

Back

If g(x) = f(-x), the graph of f is reflected over the y-axis.

Front

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

Back

It represents a horizontal translation left by c units if c > 0, and right if c < 0.