Transformations of Quadratic and Linear Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of a function, which can include shifts, stretches, compressions, and reflections.

Front

What does a horizontal shift to the right by 'h' units do to the function f(x)?

Back

The new function is g(x) = f(x - h). This shifts the graph of f(x) to the right by 'h' units.

Front

What does a horizontal shift to the left by 'h' units do to the function f(x)?

Back

The new function is g(x) = f(x + h). This shifts the graph of f(x) to the left by 'h' units.

Front

What is a vertical shift of a function?

Back

A vertical shift moves the graph of a function up or down without changing its shape. For example, g(x) = f(x) + k shifts the graph up by k units if k > 0 and down if k < 0.

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1. For example, g(x) = af(x) where a > 1 stretches the graph vertically.

Front

What does a vertical compression of a function mean?

Back

A vertical compression occurs when the output of the function is multiplied by a factor between 0 and 1. For example, g(x) = af(x) where 0 < a < 1 compresses the graph vertically.

Front

How does the graph of g(x) = f(x - 3) + 1 differ from f(x)?

Back

The graph of g(x) is shifted 3 units to the right and 1 unit up compared to f(x).

Front

What is the effect of the transformation g(x) = f(x + 7)?

Back

The graph of g(x) is shifted 7 units to the left compared to f(x).

Front

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

Back

The graph of g(x) is vertically stretched by a factor of 3 compared to f(x).

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is the highest or lowest point on the graph, depending on the direction of the parabola.