Algebra - Transformations (3.3)

Front

What is a transformation in algebra?

Back

A transformation in algebra refers to the process of changing a function's graph through operations such as shifting, stretching, compressing, or reflecting.

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically means moving it up or down on the coordinate plane without changing its shape.

Front

What is a vertical stretch?

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 is a horizontal compression?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor greater than 1, making the graph narrower.

Front

How do you represent a vertical shift of a function?

Back

A vertical shift of a function f(x) can be represented as g(x) = f(x) + k, where k is the number of units shifted up (if k > 0) or down (if k < 0).

Front

How do you represent a horizontal shift of a function?

Back

A horizontal shift of a function f(x) can be represented as g(x) = f(x - h), where h is the number of units shifted right (if h > 0) or left (if h < 0).

Front

What is the parent function for linear equations?

Back

The parent function for linear equations is f(x) = x, which represents a straight line with a slope of 1 and a y-intercept of 0.

Front

What does it mean for a graph to be steeper?

Back

A graph is steeper if it has a greater slope, meaning it rises or falls more sharply as you move along the x-axis.

Front

How do you determine the slope of a linear function?

Back

The slope of a linear function can be determined from its equation in the form g(x) = mx + b, where m represents the slope.

Front

What is the effect of multiplying a function by a factor less than 1?

Back

Multiplying a function by a factor less than 1 results in a vertical compression, making the graph shorter.