Linear, Exponential, & Quadratic Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for transformations. Examples include linear functions (y = x), quadratic functions (y = x²), and exponential functions (y = 2^x).

Front

What transformation occurs when a function is translated left?

Back

Translating a function left involves shifting the graph horizontally to the left by a certain number of units. For example, f(x) becomes f(x + c) for a left translation of c units.

Front

What does it mean to vertically stretch 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. For example, y = 2f(x) stretches the graph of f(x) vertically by a factor of 2.

Front

How do you represent a translation 5 units up in a function?

Back

To represent a translation 5 units up, you add 5 to the function. For example, if f(x) = x², the translated function is g(x) = x² + 5.

Front

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

Back

A negative sign in front of a function reflects the graph across the x-axis. For example, if f(x) = x², then -f(x) = -x² reflects the parabola downward.

Front

What transformation does g(x) = f(x - 3) represent?

Back

The transformation g(x) = f(x - 3) represents a translation of the graph of f(x) to the right by 3 units.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you identify a vertical compression in a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1. For example, y = 0.5f(x) compresses the graph of f(x) vertically by a factor of 0.5.

Front

What does the term 'translation' mean in the context of function transformations?

Back

Translation refers to shifting the graph of a function horizontally or vertically without changing its shape. It can be left/right (horizontal) or up/down (vertical).

Front

What is the parent function of an exponential function?

Back

The parent function of an exponential function is f(x) = a^x, where a > 0 and a ≠ 1. An example is f(x) = 2^x.