Linear and Quadratic Transformations

Front

What is a vertical stretch in transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller without changing its horizontal position.

Front

What does the equation g(x) = 2f(x) do to the graph of f(x)?

Back

It vertically stretches the graph of f(x) by a scale factor of 2.

Front

What is a horizontal shift in transformations?

Back

A horizontal shift occurs when the input values of a function are adjusted, moving the graph left or right on the coordinate plane.

Front

If g(x) = f(x - 3), what transformation is applied to the graph of f(x)?

Back

The graph of f(x) is shifted to the right by 3 units.

Front

What does the equation g(x) = f(x) + 2 do to the graph of f(x)?

Back

It shifts the graph of f(x) upward by 2 units.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x^2, which is a parabola opening upwards.

Front

What does the equation g(x) = f(x) - 4 represent?

Back

It represents a vertical shift of the graph of f(x) downward by 4 units.

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) across the x-axis.

Front

What does the equation g(x) = 3f(x) do to the graph of f(x)?

Back

It vertically stretches the graph of f(x) by a scale factor of 3.

Front

If g(x) = f(x + 2), what transformation is applied to the graph of f(x)?

Back

The graph of f(x) is shifted to the left by 2 units.