Translations of Functions

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x^2.

Front

What does a transformation of 'shift right 2 units' indicate for the function y = (x - 2)^2?

Back

It indicates that the graph of the function is moved 2 units to the right from the parent function.

Front

How does the transformation 'down 2' affect the graph of y = (x - 3)^3 - 2?

Back

It moves the entire graph of the function down by 2 units.

Tags

CCSS.HSF.BF.B.3

Front

What is the effect of a vertical translation of 1.5 units down on the function a(x) = x - 1.5?

Back

The graph of the function is shifted down 1.5 units compared to the parent function f(x) = x.

Front

What transformation is represented by the equation y = (x)^3 + 6?

Back

The graph is shifted up 6 units from the parent cubic function.

Tags

CCSS.HSF.BF.B.3

Front

What does the transformation 'shift right' mean in the context of the function y = (x - 4)^2?

Back

It means that the graph of the function is moved 4 units to the right from the parent quadratic function.

Front

What is a vertical translation in the context of function transformations?

Back

A vertical translation moves the graph of a function up or down without changing its shape.

Front

What is a horizontal translation in the context of function transformations?

Back

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

Front

How do you identify the direction of a transformation from a function's equation?

Back

Look for changes in the x or y values in the function's equation; positive values indicate shifts right or up, while negative values indicate shifts left or down.

Front

What is the effect of the transformation y = (x + 5)^2?

Back

The graph is shifted left 5 units from the parent function y = x^2.