transformation of functions

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 does it mean to shift a function up by 2 units?

Back

Shifting a function up by 2 units means adding 2 to the output of the function, moving the entire graph upwards.

Front

Describe the transformation of the function g(x) = 5x^2 + 2 from the parent function f(x) = x^2.

Back

Vertical Stretch of 5 and Up 2.

Front

What is the effect of subtracting a constant from a function, such as in t(x) = f(x) - 1?

Back

Subtracting a constant shifts the graph down by that constant's value.

Front

What does it mean to move a function left by 2 units?

Back

Moving a function left by 2 units means replacing x with (x + 2) in the function's equation.

Front

What is the transformation represented by k(x) = f(x) - 9?

Back

The transformation is a downward shift of 9 units.

Front

How does a vertical compression affect a function?

Back

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

Front

What is the transformation for moving a function right by 7 units?

Back

To move a function right by 7 units, replace x with (x - 7) in the function's equation.

Front

What does the equation g(x) = 5f(x) represent?

Back

This represents a vertical stretch of the function f(x) by a factor of 5.

Front

If f(x) = x^2, what is the transformation for g(x) = f(x - 3)?

Back

The transformation is a shift to the right by 3 units.