Linear Transformations

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 equations?

Back

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

Front

What happens to the graph of f(x) when we add a constant 'd' to it?

Back

The graph of f(x) shifts vertically; if 'd' is positive, it shifts up, and if 'd' is negative, it shifts down.

Front

What does g(x) = f(x - 3) represent?

Back

g(x) is the graph of f(x) shifted to the right by 3 units.

Front

What does g(x) = f(x + 3) represent?

Back

g(x) is the graph of f(x) shifted to the left by 3 units.

Front

If g(x) = f(x) + 6, how does the graph of f(x) change?

Back

The graph of f(x) shifts up by 6 units.

Front

If g(x) = f(x) - 4, how does the graph of f(x) change?

Back

The graph of f(x) shifts down by 4 units.

Front

What is the effect of multiplying f(x) by a positive constant 'a'?

Back

The graph of f(x) stretches vertically if 'a' > 1 and compresses vertically if '0 < a < 1'.

Front

What is the effect of multiplying f(x) by a negative constant?

Back

The graph of f(x) reflects over the x-axis and may stretch or compress vertically depending on the absolute value of the constant.

Front

What does the equation y = f(x) + d indicate?

Back

The graph of f(x) is shifted vertically by 'd' units; up if 'd' is positive and down if 'd' is negative.