Front

What is a transformation in mathematics?

Back

A transformation is an operation that moves or changes a shape in some way, such as translation, rotation, reflection, or dilation.

Front

Define translation in the context of transformations.

Back

Translation is a type of transformation that shifts a graph or shape horizontally and/or vertically without changing its size, shape, or orientation.

Front

What does it mean to stretch a function vertically?

Back

Stretching a function vertically means multiplying the function by a factor greater than 1, which increases the distance of points from the x-axis.

Front

What is the effect of replacing f(x) with 2f(x)?

Back

Replacing f(x) with 2f(x) vertically stretches the graph by a factor of 2.

Front

How does the graph of f(x) = x change when it is transformed to g(x) = f(x) - 3?

Back

The graph of f(x) = x shifts down by 3 units.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which represents a straight line through the origin with a slope of 1.

Front

What does the notation g(x) = f(x) + 7 indicate about the transformation?

Back

This notation indicates that the graph of f(x) is translated upward by 7 units.

Front

If g(x) = f(x - 4), what transformation occurs?

Back

The graph of f(x) is translated to the right by 4 units.

Front

What is the result of the expression 4x - 2x + 2 - 3?

Back

The result is 2x - 1.

Front

What does a negative coefficient in front of a function indicate?

Back

A negative coefficient reflects the graph across the x-axis.