Transformations of Functions

Front

What is a vertical translation of a function?

Back

A vertical translation of a function moves the graph up or down without changing its shape.

Front

How does adding a constant to a function affect its graph?

Back

Adding a constant to a function shifts the graph vertically. For example, f(x) + c shifts the graph up by c units if c > 0 and down by c units if c < 0.

Front

What is a horizontal translation of a function?

Back

A horizontal translation of a function moves the graph left or right without changing its shape.

Front

How does adding a constant inside the function argument affect its graph?

Back

Adding a constant inside the function argument, like f(x + c), shifts the graph left by c units if c > 0 and right by c units if c < 0.

Front

What does it mean to reflect a function across the y-axis?

Back

Reflecting a function across the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y). This is represented by f(-x).

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph across the x-axis.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The vertex of a quadratic function in standard form can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the effect of a vertical stretch or compression on a function?

Back

A vertical stretch occurs when a function is multiplied by a factor greater than 1, making it taller. A vertical compression occurs when it is multiplied by a factor between 0 and 1, making it shorter.

Front

What is the relationship between the transformations of f(x) and g(x) if g(x) = f(x - 3) + 2?

Back

g(x) represents a horizontal translation of f(x) to the right by 3 units and a vertical translation up by 2 units.