Linear Transformations Review

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

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

Front

How does the function g(x) = f(x) + c transform the graph of f(x)?

Back

The graph of f(x) is shifted vertically by c units. If c is positive, it shifts up; if c is negative, it shifts down.

Front

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

Back

The graph of f(x) is shifted horizontally by c units. If c is positive, it shifts right; if c is negative, it shifts left.

Front

What effect does multiplying a function by a constant have?

Back

Multiplying a function by a constant a (g(x) = a * f(x)) results in a vertical stretch if |a| > 1, and a vertical compression if 0 < |a| < 1.

Front

What is the transformation represented by g(x) = f(x) - 6?

Back

The graph of f(x) is shifted down 6 units.

Front

What is the transformation represented by g(x) = f(x + 3)?

Back

The graph of f(x) is shifted left 3 units.

Front

What is the transformation represented by g(x) = 4f(x)?

Back

The graph of f(x) is vertically stretched by a factor of 4.

Front

What is the transformation represented by g(x) = (1/4)f(x)?

Back

The graph of f(x) is vertically compressed by a factor of 1/4.

Front

How does the function y = x + 7 shift from y = x?

Back

The graph shifts up 7 units.