Writing Transformations of Functions

Front

What is the effect of adding a constant to a function, such as in g(x) = f(x) + c?

Back

The graph of the function shifts vertically. If c > 0, the graph shifts up; if c < 0, it shifts down.

Front

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

Back

The graph of the function shifts horizontally. If c > 0, the graph shifts to the right; if c < 0, it shifts to the left.

Front

What is the effect of multiplying a function by a constant, such as in g(x) = k * f(x)?

Back

If k > 1, the graph undergoes a vertical stretch; if 0 < k < 1, it undergoes a vertical shrink.

Front

Describe the transformation of g(x) = f(x) + 3.

Back

The graph of f(x) shifts vertically up by 3 units.

Front

Describe the transformation of g(x) = f(x - 5).

Back

The graph of f(x) shifts horizontally to the right by 5 units.

Front

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

Back

The graph of f(x) is reflected over the x-axis.

Front

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

Back

The graph of f(x) is reflected over the y-axis.

Front

What is the effect of a vertical shift on the function f(x) = x^2?

Back

A vertical shift changes the y-values of the function, moving the graph up or down.

Front

What is the transformation of g(x) = 2f(x) when f(x) = x^2?

Back

The graph of f(x) is vertically stretched by a factor of 2.

Front

How does the transformation g(x) = f(x + 4) affect the graph of f(x)?

Back

The graph shifts horizontally to the left by 4 units.