Vertical Shifts in Functions

The video tutorial explains vertical shifts in functions, comparing them with horizontal shifts. It highlights the role of the constant k in vertical transformations, showing how adding or subtracting k affects the function's graph. Examples using quadratic and exponential functions illustrate vertical shifts up and down. The tutorial emphasizes understanding these concepts for better graphing skills.

What is the main difference between vertical and horizontal shifts in functions?

• Horizontal shifts involve adding or subtracting outside the function.

• Vertical shifts involve changing the x-values.

• Horizontal shifts involve changing the y-values.

• Vertical shifts involve adding or subtracting outside the function.

When applying a vertical shift, what operation is performed on the function?

• Multiply by a constant.

• Square the function.

• Add or subtract a constant.

• Divide by a constant.

In a vertical shift, where is the constant added or subtracted?

• At the vertex.

• At the origin.

• Outside the function.

• Inside the function.

What happens to a quadratic function when a positive constant is added outside the function?

• It shifts downwards.

• It shifts upwards.

• It shifts to the left.

• It shifts to the right.

How does adding a constant outside an exponential function affect its graph?

• The graph shifts down.

• The graph shifts up.

• The graph shifts right.

• The graph shifts left.

What is the effect of adding a positive constant to a function?

• The graph shifts right.

• The graph shifts up.

• The graph shifts down.

• The graph shifts left.

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

• The graph shifts right.

• The graph shifts up.

• The graph shifts down.

• The graph shifts left.

In the expression f(x) = x^2 + k, what does 'k' represent?

• A reflection.

• A horizontal shift.

• A vertical shift.

• A rotation.

In the function f(x) = 5 + 3^x, what does the '5' indicate?

• A reflection.

• A vertical shift down.

• A vertical shift up.

• A horizontal shift.

In the context of vertical shifts, what does 'k' typically represent?

• A horizontal shift.

• A vertical shift.

• A reflection.

• A rotation.