Transformation of Functions - Practice

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 left or right?

Back

Translating a function left or right involves shifting the graph horizontally. A positive value inside the function's argument (e.g., f(x + c)) translates it left by c units, while a negative value (e.g., f(x - c)) translates it right by c units.

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 is a reflection of a function over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph, effectively flipping it upside down.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x², which is the simplest form of a quadratic function.

Front

How do you identify a quadratic function translated left 4 units?

Back

A quadratic function translated left 4 units can be represented as y = (x + 4)², shifting the vertex of the parabola 4 units to the left.

Front

What does the notation f(x + c) indicate?

Back

The notation f(x + c) indicates a horizontal translation of the function f(x) to the left by c units.

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign in front of a function (e.g., -f(x)) reflects the graph over the x-axis.

Front

What does a scale factor of 2 indicate in a function transformation?

Back

A scale factor of 2 indicates a vertical stretch of the function, making it twice as tall.

Front

What is the transformation represented by m(x) = f(x + 1)?

Back

The transformation represented by m(x) = f(x + 1) is a translation of the function f(x) 1 unit to the left.