Transformations of Functions

Front

What is a transformation of a function?

Back

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

Front

What does it mean to translate a function up or down?

Back

Translating a function up means adding a constant to the function's output, while translating it down means subtracting a constant from the output.

Front

Back

The graph of the function is translated vertically by k units. If k is positive, the graph moves up; if k is negative, it moves down.

Front

Back

This represents a horizontal translation of the graph. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is a reflection in the x-axis?

Back

A reflection in the x-axis occurs when the output of the function is multiplied by -1, resulting in the graph being flipped over the x-axis.

Front

What does a vertical stretch by a factor of a > 1 do to the graph?

Back

A vertical stretch by a factor of a > 1 makes the graph taller, pulling points away from the x-axis.

Front

What is the effect of a vertical shrink by a factor of 0 < a < 1?

Back

A vertical shrink by a factor of 0 < a < 1 compresses the graph towards the x-axis, making it shorter.

Front

Back

This transformation reflects the graph over the x-axis.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Back

This indicates a horizontal translation of the graph to the left by 5 units.