Linear Translations Flashcard

Front

What is the linear parent function?

Back

The linear parent function is f(x) = x, which represents a straight line with a slope of 1 and a y-intercept of 0.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x) - 7?

Back

The graph is shifted vertically down by 7 units.

Front

Describe the transformation when f(x) = x is changed to g(x) = f(x - 3).

Back

The graph is shifted horizontally to the right by 3 units.

Front

If the graph of f(x) = x is shifted 7 units up, what is the new function?

Back

g(x) = f(x) + 7, or g(x) = x + 7.

Front

What does it mean when a function is horizontally compressed by a factor of 3?

Back

It means that the x-values of the function are multiplied by 3, making the graph narrower.

Front

What is the result of transforming f(x) = x to g(x) = f(x) + 6?

Back

The graph is shifted vertically up by 6 units.

Front

What does the transformation g(x) = f(x + 6) indicate?

Back

The graph is shifted horizontally to the left by 6 units.

Front

How do you identify a vertical translation in a function?

Back

A vertical translation occurs when a constant is added or subtracted from the function, affecting the y-values.

Front

How do you identify a horizontal translation in a function?

Back

A horizontal translation occurs when a constant is added or subtracted from the x-variable inside the function.

Front

What is the effect of the transformation g(x) = f(3x) on the graph of f(x) = x?

Back

The graph is horizontally compressed by a factor of 3.