Linear Transformations and Parent Function

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Front

What is the parent function of linear functions?

Back

f(x) = x

Front

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

Back

g(x) is shifted right 3 units.

Front

What does a vertical translation of a graph mean?

Back

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

Front

If the graph of f(x) is translated 2 units up, what is the new function?

Back

g(x) = f(x) + 2.

Front

What is the effect of a horizontal translation of 3 units to the left on the function f(x)?

Back

The new function is g(x) = f(x + 3).

Front

What does the equation y = (x - 3) + 5 represent in terms of transformations?

Back

It represents a shift 3 units right and 5 units up from the parent function.

Front

What is a reflection in the context of graph transformations?

Back

A reflection flips the graph over a specified axis, such as the x-axis or y-axis.

Front

How does the function f(x) = x - 2 transform the parent function?

Back

It shifts the graph of the parent function down 2 units.

Front

What is the effect of a vertical stretch by a factor of 2 on the function f(x)?

Back

The new function is g(x) = 2f(x), which makes the graph taller.