Horizontal Translations of Linear Functions

Front

What is a horizontal translation of a function?

Back

A horizontal translation shifts the graph of a function left or right without changing its shape.

Front

If the function is g(x) = f(x - c), what type of translation occurs?

Back

A horizontal translation to the right by c units.

Front

If the function is g(x) = f(x + c), what type of translation occurs?

Back

A horizontal translation to the left by c units.

Front

What does the term 'parent function' refer to?

Back

The simplest form of a function, from which more complex functions can be derived.

Front

What is the effect of a positive value in the function g(x) = f(x - c)?

Back

It translates the graph of f(x) to the right by c units.

Front

What is the effect of a negative value in the function g(x) = f(x + c)?

Back

It translates the graph of f(x) to the left by c units.

Front

How does the function g(x) = 3/4f(x) transform the graph of f(x)?

Back

It compresses the graph vertically by a factor of 3/4.

Front

What happens to the graph of f(x) when g(x) = f(x - 9.5)?

Back

The graph of f(x) shifts to the right by 9.5 units.

Front

What happens to the graph of f(x) when g(x) = f(x + 100)?

Back

The graph of f(x) shifts to the left by 100 units.

Front

If g(x) = f(x + 9.5), what is the translation direction and distance?

Back

The graph shifts to the left by 9.5 units.