Transformations Algebra 2

Front

What is a transformation in algebra?

Back

A transformation in algebra refers to the process of changing the position, size, or shape of a graph. This can include translations, reflections, stretches, and compressions.

Front

What does a translation of a graph involve?

Back

A translation involves shifting the graph of a function horizontally and/or vertically without changing its shape.

Front

How does the equation g(x) = (x - 3)^2 transform the graph of f(x) = x^2?

Back

The equation g(x) = (x - 3)^2 translates the graph of f(x) = x^2 to the right by 3 units.

Front

What is the effect of a vertical stretch on a graph?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

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

Back

The equation g(x) = 2f(x) vertically stretches the graph of f(x) by a scale factor of 2.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you represent a vertical shift in a function?

Back

A vertical shift is represented by adding or subtracting a constant from the function, e.g., f(x) + k, where k is the shift amount.

Front

What does the notation |x| represent in a function?

Back

The notation |x| represents the absolute value of x, which is the distance of x from 0 on the number line, always non-negative.

Front

How does the equation g(x) = |x - 2| transform the graph of f(x) = |x|?

Back

The equation g(x) = |x - 2| translates the graph of f(x) = |x| to the right by 2 units.

Front

What is the effect of moving a graph left or right?

Back

Moving a graph left or right involves changing the input value of the function, which translates the graph horizontally.