24-25 Alg1 3-7 FLASHCARD - Linear Transformations

Front

What is the parent function of a linear equation?

Back

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

Front

What does a vertical shift of +10 units indicate in a linear transformation?

Back

It indicates that the graph of the function is shifted up 10 units.

Front

What does a vertical shift of -2 units indicate in a linear transformation?

Back

It indicates that the graph of the function is shifted down 2 units.

Front

How does the transformation g(x) = -f(x) - 3 affect the graph of the parent function f(x) = x?

Back

It reflects the graph over the x-axis and shifts it down 3 units.

Front

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

Back

A vertical stretch occurs when the slope of the line increases, making the graph steeper.

Front

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

Back

It results in a vertical stretch of the graph.

Front

What is the effect of multiplying a linear function by a factor between 0 and 1?

Back

It results in a vertical compression of the graph.

Front

What is the significance of the term 'parent function' in mathematics?

Back

The parent function is the simplest form of a function type, from which transformations can be derived.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the transformation represented by the equation y = mx + b?

Back

In this equation, m represents the slope and b represents the y-intercept, indicating how the line is positioned on the graph.