Understanding Graph Translations

The video tutorial explains the concept of function translations, focusing on how adding or subtracting constants to a function or its input affects the graph's position. Vertical translations occur when constants are added or subtracted from the function value, shifting the graph up or down. Horizontal translations happen when constants are added or subtracted from the input, shifting the graph left or right. The tutorial uses animations and examples, including a quadratic function, to illustrate these concepts.

What type of transformation occurs when a constant is added to f(x)?

• The graph shifts up.

• The graph shifts left.

• The graph shifts down.

• The graph shifts right.

If f(x) is subtracted by a constant, what happens to the graph?

• The graph shifts up.

• The graph shifts down.

• The graph shifts left.

• The graph shifts right.

What happens to the graph when a constant is subtracted from x?

• The graph shifts down.

• The graph shifts up.

• The graph shifts right.

• The graph shifts left.

When a constant is added to x, in which direction does the graph move?

• The graph shifts down.

• The graph shifts up.

• The graph shifts right.

• The graph shifts left.

For the function f(x) = x^2, what is the result of f(x + 4)?

• y = (x - 4)^2

• y = x^2 - 4

• y = x^2 + 4

• y = (x + 4)^2

What is the transformation for f(x - 4) when f(x) = x^2?

• y = x^2 - 4

• y = (x + 4)^2

• y = x^2 + 4

• y = (x - 4)^2

How does f(x + 4) affect the graph of f(x) = x^2?

• The graph shifts left 4 units.

• The graph shifts up 4 units.

• The graph shifts right 4 units.

• The graph shifts down 4 units.

What is the effect of f(x - 4) on the graph of f(x) = x^2?

• The graph shifts left 4 units.

• The graph shifts down 4 units.

• The graph shifts up 4 units.

• The graph shifts right 4 units.

What is the result of f(x) = x^2 when a constant is added to the function value?

• The graph shifts left.

• The graph shifts right.

• The graph shifts up.

• The graph shifts down.

What is the result of f(x) = x^2 when a constant is subtracted from the function value?

• The graph shifts down.

• The graph shifts up.

• The graph shifts right.

• The graph shifts left.