24-25 Alg1 3-7 FLASHCARD - Linear Transformations

Front

What is a vertical stretch in linear transformations?

Back

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

Front

What does a vertical compression do to a graph?

Back

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

Front

How does shifting a graph up affect its equation?

Back

Shifting a graph up by 'k' units adds 'k' to the output of the function: if f(x) is the original function, the new function is g(x) = f(x) + k.

Front

What is the effect of shifting a graph down?

Back

Shifting a graph down by 'k' units subtracts 'k' from the output of the function: g(x) = f(x) - k.

Front

What does the transformation g(x) = f(x - 4) represent?

Back

This transformation shifts the graph of f(x) to the right by 4 units.

Front

What does the transformation g(x) = f(3x) do to the graph?

Back

This transformation compresses the graph horizontally by a factor of 3.

Front

What is the effect of the transformation g(x) = -f(x)?

Back

This transformation reflects the graph of f(x) across the x-axis.

Front

How do you represent a vertical stretch by a factor of 4?

Back

A vertical stretch by a factor of 4 is represented as g(x) = 4f(x).

Front

What does the equation g(x) = f(x) + 3 do to the graph of f(x)?

Back

This equation shifts the graph of f(x) up by 3 units.

Front

If f(x) = x, what is g(x) if the graph is shifted 7 units up and compressed horizontally by a factor of 3?

Back

g(x) = f(3x) + 7.