Practice: Function Transformations

Front

What is the transformation of the function g(x) = cos(x + a) - b compared to the parent function p(x) = cos(x)?

Back

The graph of g(x) is translated left a units and down b units.

Front

Describe the transformation of g(x) = f(x - 1) - 5 in relation to f(x).

Back

The graph of f(x) is translated right 1 unit and down 5 units.

Front

If f(x) = x^2, what is the transformation for g(x) = x^2 - 5?

Back

The graph of f(x) is translated down 5 units.

Front

What does the transformation p(x) = f(x + 3) indicate about the graph of f(x)?

Back

The graph of f(x) is translated left 3 units.

Front

How does the function g(x) = (x + 4)^2 transform the graph of f(x) = x^2?

Back

The graph of f(x) is translated left 4 units.

Front

What is the effect of a positive constant 'a' in the transformation g(x) = f(x + a)?

Back

It translates the graph of f(x) left a units.

Front

What is the effect of a negative constant 'b' in the transformation g(x) = f(x) - b?

Back

It translates the graph of f(x) down b units.

Front

If g(x) = f(x) + b, what transformation does this represent?

Back

The graph of f(x) is translated up b units.

Front

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

Back

The graph of f(x) is translated right a units.

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.