Transformations of Functions

Front

What is a vertical translation of a function?

Back

A vertical translation moves the graph of a function up or down. For example, if you add a constant 'k' to a function f(x), the graph shifts up by 'k' units if k > 0, and down by 'k' units if k < 0.

Front

Back

The graph of the function f(x) is shifted 3 units up.

Front

What is a horizontal translation of a function?

Back

A horizontal translation moves the graph of a function left or right. If you replace x with (x - h) in f(x), the graph shifts right by 'h' units if h > 0, and left by 'h' units if h < 0.

Front

Back

The graph of the function g(x) is shifted 4 units left and 6 units down.

Front

What is the general form of a quadratic function?

Back

Front

Which equation represents a quadratic function translated up 5 units?

Back

Front

Back

The graph of the function f(x) is shifted 2 units to the right.

Front

Back

The graph of the function f(x) is shifted 3 units to the right and 5 units up.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph across the x-axis.

Front

Back

The graph of the function f(x) is reflected across the y-axis.