Graph Translations and Shifts

The video tutorial explains how translations and shifts affect the graph of a function. It starts with a basic parabola, f(x) = x^2, and demonstrates vertical shifts using g(x) = x^2 + 1 and h(x) = x^2 - 3. The tutorial then covers horizontal shifts with j(x) = (x + 2)^2 and k(x) = (x - 1)^2, emphasizing the common mistake of misinterpreting the direction of shifts. The key takeaway is the mnemonic: 'add to Y, go high; add to X, go west.'

What is the initial example used to explain graph translations?

• A cubic function

• A linear function

• A sine wave

• A parabola

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

• It shifts to the right

• It moves down

• It moves up

• It shifts to the left

How does subtracting a constant from a function affect its graph?

• The graph shifts upwards

• The graph shifts downwards

• The graph shifts to the left

• The graph shifts to the right

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

• The graph shifts to the left

• The graph shifts upwards

• The graph shifts downwards

• The graph shifts to the right

When a constant is subtracted from the x-value, in which direction does the graph shift?

• To the left

• Downwards

• To the right

• Upwards

What is the x-value shift when the function is (x + 2)^2?

• 2 units to the right

• 2 units downwards

• 2 units to the left

• 2 units upwards

What happens to the graph when you add a constant to the x-value?

• It shifts to the right

• It shifts to the left

• It shifts downwards

• It shifts upwards

What is the classic algebra mistake number eight related to?

• Incorrectly shifting graphs

• Misplacing decimal points

• Mixing up addition and subtraction

• Forgetting to square terms

What mnemonic is suggested to remember the direction of graph shifts?

• Add to Y go high, add to X go west

• Subtract from Y go low, subtract from X go east

• Multiply Y go high, divide X go west

• Add to Y go east, add to X go high

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

• The graph shifts downwards

• The graph shifts to the left

• The graph shifts upwards

• The graph shifts to the right