transformations

Front

What is a transformation in mathematics?

Back

A transformation is a function that changes the position, size, or shape of a graph.

Front

What does it mean to translate a function?

Back

To translate a function means to shift its graph horizontally and/or vertically without changing its shape.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

How does the equation y = |x + 4| + 7 transform the parent function y = |x|?

Back

It translates the graph 4 units left and 7 units up.

Front

What is a vertical translation?

Back

A vertical translation shifts the graph of a function up or down.

Front

What is a horizontal translation?

Back

A horizontal translation shifts the graph of a function left or right.

Front

How do you translate the function f(x) = 2x + 3 down 2 units?

Back

The new function is g(x) = 2x + 1.

Front

What effect does the equation y = (x - 4)² + 7 have on the graph of y = x²?

Back

It translates the graph 4 units right and 7 units up.

Front

What is a reflection in mathematics?

Back

A reflection flips a graph over a specified line, such as the x-axis or y-axis.

Front

What does the equation y = |x - 3| + 4 represent?

Back

It represents a translation of the parent function y = |x|, shifted 3 units right and 4 units up.