Vertical and Horizontal Translations

Front

What is a horizontal translation?

Back

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

Front

How does the function g(x) = (x + 4)² relate to f(x) = x²?

Back

g(x) is a horizontal translation of f(x) = x², shifting it 4 units to the left.

Front

What is a vertical translation?

Back

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

Front

How does the function y = x - 7 shift from the parent function y = x?

Back

It shifts down 7 units.

Front

What is the effect of adding a positive number to the function f(x)?

Back

It results in a vertical translation upwards.

Front

What is the effect of subtracting a positive number from the function f(x)?

Back

It results in a vertical translation downwards.

Front

Which equation describes the transformation of shifting f(x) = x² two units right?

Back

The equation is (x - 2)².

Front

What does the equation g(x) = (x - 3)² represent?

Back

It represents a horizontal translation of f(x) = x², shifting it 3 units to the right.

Front

If f(x) = x², what is the graph of g(x) = x² + 5?

Back

It is a vertical translation of f(x) = x², shifting it 5 units up.

Front

What is the general form of a horizontal translation?

Back

g(x) = f(x - h) where h is the number of units to shift.