Linear Transformations (Trans. & Dilations)

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 effect does a reflection across the x-axis have on a function f(x)?

Back

It transforms the function to g(x) = -f(x), flipping the graph over the x-axis.

Front

How does a vertical compression by a factor of k affect the function f(x)?

Back

It transforms the function to g(x) = kf(x), where 0 < k < 1, making the graph closer to the x-axis.

Front

What is the result of shifting the graph of f(x) vertically by c units?

Back

The new function is g(x) = f(x) + c, where c is positive for an upward shift and negative for a downward shift.

Front

What does the equation g(x) = f(kx) represent?

Back

It represents a horizontal compression or expansion of the function f(x) depending on the value of k.

Front

What is the effect of a horizontal compression by a factor of 3 on the function f(x)?

Back

The new function is g(x) = f(3x), which compresses the graph towards the y-axis.

Front

What does the transformation g(x) = -f(x) - 3 do to the graph of f(x)?

Back

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

Front

How do you represent a vertical shift of a function f(x) down by 4 units?

Back

The new function is g(x) = f(x) - 4.

Front

What is the parent function for linear transformations?

Back

The parent function for linear transformations is f(x) = x.

Front

What does the transformation g(x) = f(3x) + 7 indicate about the graph of f(x)?

Back

It indicates a horizontal compression by a factor of 3 and a vertical shift upward by 7 units.