Writing Transformations of Functions

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What does the transformation f(x) = h(x) + k represent?

Back

This transformation shifts the graph of f(x) vertically by k units. If k is positive, the graph moves up; if k is negative, it moves down.

Front

What does the transformation f(x) = h(x - c) represent?

Back

This transformation shifts the graph of f(x) horizontally by c units. If c is positive, the graph moves right; if c is negative, it moves left.

Front

What is a vertical shrink of a function?

Back

A vertical shrink occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

Describe the transformation of f(x) = x^2 to g(x) = 3x^2.

Back

This represents a vertical stretch by a factor of 3.

Front

What does the transformation g(x) = f(x) - 5 indicate?

Back

This transformation shifts the graph of f(x) down by 5 units.

Front

What does the transformation g(x) = f(x + 3) indicate?

Back

This transformation shifts the graph of f(x) left by 3 units.

Front

How do you represent a horizontal stretch of a function?

Back

A horizontal stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider.

Front

What is the effect of the transformation g(x) = 2f(x) + 1?

Back

This transformation represents a vertical stretch by a factor of 2 and shifts the graph up by 1 unit.

Front

What does the transformation g(x) = f(2x) represent?

Back

This transformation represents a horizontal shrink by a factor of 1/2.