Graphing Square and Cube Root Functions

Front

What is the general form of a square root function?

Back

f(x) = √(x - h) + k, where (h, k) is the vertex.

Front

What does the 'h' value in the square root function f(x) = √(x - h) + k represent?

Back

'h' represents the horizontal shift of the graph. If h is positive, the graph shifts to the right; if negative, it shifts to the left.

Front

What does the 'k' value in the square root function f(x) = √(x - h) + k represent?

Back

'k' represents the vertical shift of the graph. If k is positive, the graph shifts up; if negative, it shifts down.

Front

How does the graph of f(x) = √(x) compare to f(x) = √(x - 4)?

Back

f(x) = √(x - 4) shifts the graph of f(x) = √(x) 4 units to the right.

Front

What effect does a negative sign in front of the square root function have, such as in f(x) = -√(x)?

Back

It reflects the graph over the x-axis.

Front

What is the general form of a cube root function?

Back

f(x) = ∛(x - h) + k, where (h, k) is the point of inflection.

Front

How does the graph of f(x) = ∛(x) compare to f(x) = ∛(x + 3)?

Back

f(x) = ∛(x + 3) shifts the graph of f(x) = ∛(x) 3 units to the left.

Front

What does the point of inflection in a cube root function indicate?

Back

It is the point where the graph changes direction and is typically at (h, k).

Front

What transformation does the function f(x) = √(x - 5) - 1 represent?

Back

It shifts the graph of f(x) = √(x) 5 units to the right and 1 unit down.

Front

If a function is written as f(x) = -√(x + 1) + 3, what transformations have occurred?

Back

The graph is shifted 1 unit to the left, reflected over the x-axis, and shifted up 3 units.