Linear & Quad Transformations (a & d)

Front

What is the effect of adding a constant to a function, such as in g(x) = f(x) + 4?

Back

The graph of the function shifts vertically. In this case, it shifts 4 units up.

Front

What happens to the graph of a quadratic function when the leading coefficient is greater than 1, such as in y = 2x^2?

Back

The parabola becomes stretched, making it skinnier.

Front

What is the effect of subtracting a constant from a function, such as in g(x) = f(x) - 4?

Back

The graph of the function shifts vertically. In this case, it shifts 4 units down.

Front

What does the equation g(x) = 6f(x) indicate about the transformation of the parent function?

Back

The graph is stretched vertically by a factor of 6.

Front

How does the equation f(x) = -x^2 transform the parent function f(x) = x^2?

Back

It reflects the graph over the x-axis.

Front

What is a vertical stretch in the context of quadratic functions?

Back

A vertical stretch occurs when the leading coefficient of the quadratic function is greater than 1.

Front

What is a vertical compression in the context of quadratic functions?

Back

A vertical compression occurs when the leading coefficient of the quadratic function is between 0 and 1.

Front

What does a horizontal shift to the left look like in a function?

Back

It occurs when the function is in the form g(x) = f(x + c) where c > 0.

Front

What does a horizontal shift to the right look like in a function?

Back

It occurs when the function is in the form g(x) = f(x - c) where c > 0.

Front

What is the effect of a negative leading coefficient in a quadratic function?

Back

It reflects the graph over the x-axis.