Function Transformations

Front

What is the effect of the transformation g(x) = f(x) + 2 on the graph of f(x)?

Back

The graph of f(x) is shifted up 2 units.

Front

How does reflecting a function over the x-axis affect its graph?

Back

It inverts the graph, changing all positive y-values to negative and vice versa.

Front

What does a vertical stretch by a scale factor of 3 do to the graph of f(x)?

Back

It makes the graph taller, multiplying all y-values by 3.

Front

Describe the transformation represented by g(x) = f(x) - 1.

Back

The graph of f(x) is shifted down 1 unit.

Front

What is the transformation sequence for g(x) = -3f(x) + 8?

Back

Reflect over the x-axis, vertically stretch by a factor of 3, and shift up 8 units.

Front

What does the transformation g(x) = 1/5f(x) indicate about the graph of f(x)?

Back

It indicates a vertical compression by a factor of 1/5.

Front

How do you interpret the transformation g(x) = f(x - 4)?

Back

The graph of f(x) is shifted 4 units to the right.

Front

What is the effect of a negative sign in front of a function, such as g(x) = -f(x)?

Back

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

Front

What does it mean to compress a graph vertically by a factor of 1/2?

Back

It reduces the height of the graph, making it closer to the x-axis.

Front

If g(x) = f(x) + c, what does the constant c represent?

Back

The constant c represents a vertical shift of the graph; positive c shifts up, negative c shifts down.