Graphing Radical Functions (includes Domain & Range)

Front

What is the parent function of square root functions?

Back

f(x) = √x

Front

Describe the transformation of g(x) = -3√(x-2)+1 in terms of f(x) = √x.

Back

Reflects over x-axis, vertical stretch by 3, right 2, up 1.

Front

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

Back

[0, ∞) - x must be greater than or equal to 0.

Front

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

Back

[0, ∞) - output values start from 0 and go to infinity.

Front

How does the graph of f(x) = √(x) change when transformed to g(x) = -√(x)?

Back

The graph reflects over the x-axis.

Front

What effect does the transformation g(x) = 2√(x) have on the graph of f(x) = √(x)?

Back

Vertical stretch by a factor of 2.

Front

What is the domain of the function g(x) = -3√(x-2)+1?

Back

[2, ∞) - x must be greater than or equal to 2.

Front

What is the range of the function g(x) = -3√(x-2)+1?

Back

(-∞, 1] - output values start from negative infinity and go up to 1.

Front

How does the graph of f(x) = √(x) change when transformed to g(x) = √(x-3)?

Back

The graph shifts 3 units to the right.

Front

What is the effect of the negative sign in g(x) = -√(x-2)+1 on the graph of f(x) = √(x)?

Back

The graph reflects over the x-axis and shifts up 1 unit.