Graph Shifts and Translations

The video tutorial explains how translations and shifts affect the graph of a parabola. It covers vertical shifts using G(x) = x^2 + 1 and H(x) = x^2 - 3, and horizontal shifts using J(x) = (x + 2)^2 and K(x) = (x - 1)^2. The tutorial emphasizes understanding the direction of shifts and common mistakes, using the mnemonic 'add to Y go high, add to X go west'.

What is the basic function used to introduce graph translations?

• Linear function

• Quadratic function

• Cubic function

• Exponential function

What happens to the graph of a function when a constant is added to the function itself?

• The graph shifts upwards

• The graph shifts downwards

• The graph shifts to the right

• The graph shifts to the left

If a function is modified by subtracting a constant from it, what is the effect on the graph?

• The graph shifts upwards

• The graph shifts downwards

• The graph shifts to the left

• The graph shifts to the right

How does adding a constant to the x-value of a function affect its graph?

• The graph shifts to the right

• The graph shifts upwards

• The graph shifts downwards

• The graph shifts to the left

What is the effect of subtracting a constant from the x-value of a function?

• The graph shifts to the left

• The graph shifts to the right

• The graph shifts upwards

• The graph shifts downwards

What is a common mistake when interpreting horizontal shifts in graphs?

• Thinking the graph does not shift

• Thinking the graph shifts in the opposite direction

• Thinking the graph shifts downwards

• Thinking the graph shifts upwards

What mnemonic can help remember the direction of graph shifts?

• Subtract from X, go high; subtract from Y, go west

• Subtract from Y, go high; subtract from X, go west

• Add to X, go high; add to Y, go west

• Add to Y, go high; add to X, go west

What happens to the graph of a function when a constant is subtracted from the x-value?

• The graph shifts downwards

• The graph shifts to the left

• The graph shifts to the right

• The graph shifts upwards

Which of the following is NOT a result of adding a constant to the x-value?

• The graph shifts to the right

• The graph shifts downwards

• The graph shifts upwards

• The graph shifts to the left

What is the effect of adding a constant to the y-value of a function?

• The graph shifts downwards

• The graph shifts upwards

• The graph shifts to the right

• The graph shifts to the left