Transformation of Functions

Front

What is a vertical stretch in the context of function transformations?

Back

A vertical stretch occurs when a function is multiplied by a factor greater than 1, making the graph taller.

Front

What does it mean to translate a function vertically?

Back

Translating a function vertically means shifting the graph up or down along the y-axis.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function translates the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

How does the equation g(x) = 5x² + 2 transform the parent function f(x) = x²?

Back

It represents a vertical stretch by a factor of 5 and a vertical shift up by 2.

Front

What is a horizontal translation in function transformations?

Back

A horizontal translation shifts the graph left or right along the x-axis.

Front

How do you translate a quadratic function left by 4 units?

Back

To translate a quadratic function left by 4 units, you replace x with (x + 4) in the equation.

Front

What is the effect of a negative sign in front of a quadratic function?

Back

A negative sign reflects the graph across the x-axis.

Front

What does the equation y = -(x - 2)² + 4 represent?

Back

It represents a downward-opening parabola with its vertex at (2, 4).

Front

How do you identify the vertex of a quadratic function in vertex form?

Back

In vertex form, y = a(x - h)² + k, the vertex is at the point (h, k).