Graphing Square and Cube Root Functions

Front

What is the parent function of square root functions?

Back

f(x) = √x

Front

What is the parent function of cube root functions?

Back

f(x) = ∛x

Front

What does a vertical stretch by a factor of 2 do to the graph of f(x) = √x?

Back

It makes the graph steeper, stretching it vertically.

Front

What is the effect of translating a graph down 5 units?

Back

Every point on the graph moves down 5 units.

Front

How do you reflect a graph over the x-axis?

Back

Multiply the function by -1, changing f(x) to -f(x).

Front

What is the domain of the square root function f(x) = √x?

Back

x ≥ 0 (only non-negative real numbers).

Front

What is the range of the square root function f(x) = √x?

Back

y ≥ 0 (only non-negative real numbers).

Front

What is the domain of the cube root function f(x) = ∛x?

Back

All real numbers (x can be any real number).

Front

What is the range of the cube root function f(x) = ∛x?

Back

All real numbers (y can be any real number).

Front

If f(x) = √(x - 1) + 3, what transformation does this represent?

Back

Shifted right 1 unit and up 3 units.