6.1 Square Root PF / B Transformation

Front

What is the parent function of a square root?

Back

The parent function of a square root is f(x) = √x.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

How does a vertical stretch affect the graph of a function?

Back

A vertical stretch multiplies the y-values of the function by a factor greater than 1, making the graph taller.

Front

What transformation occurs when a function is shifted right by h units?

Back

Shifting a function right by h units means replacing x with (x - h) in the function's equation.

Front

What transformation occurs when a function is shifted down by k units?

Back

Shifting a function down by k units means subtracting k from the function's output.

Front

How do you determine the domain of a square root function?

Back

The domain of a square root function is all x-values for which the expression inside the square root is non-negative.

Front

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

Back

The range of f(x) = √x is [0, ∞) because the output of the square root function is always non-negative.

Front

What does the equation g(x) = -3√(x-2)+1 represent in terms of transformations of f(x) = √x?

Back

g(x) reflects f(x) over the x-axis, vertically stretches it by a factor of 3, shifts it right by 2 units, and shifts it up by 1 unit.

Front

How do you shift a radical equation left by 3 units?

Back

To shift a radical equation left by 3 units, replace x with (x + 3) in the equation.

Front

What is the effect of a vertical compression on a function?

Back

A vertical compression multiplies the y-values of the function by a factor between 0 and 1, making the graph shorter.