Square Root Transformations

Front

What is the square root parent function?

Back

The square root parent function is f(x) = √x, which produces a graph that starts at the origin (0,0) and increases gradually, forming half of a sideways parabola.

Front

How does the graph of f(x) = √x transform to g(x) = -3√(x-2)+1?

Back

g(x) reflects over the x-axis, has a vertical stretch by 3, shifts right by 2 units, and shifts up by 1 unit.

Front

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

Back

The range is (-∞, 0].

Front

What does a vertical stretch by a factor of 3 do to the graph of a function?

Back

It makes the graph steeper, increasing the distance between points on the graph.

Front

What is the effect of reflecting a graph over the x-axis?

Back

It flips the graph upside down.

Front

What is the domain of the function f(x) = √(x-2)?

Back

The domain is [2, ∞) because the expression under the square root must be non-negative.

Front

How do you identify the vertex of the transformed function g(x) = -3√(x-2)+1?

Back

The vertex is at the point (2, 1).

Front

What is the effect of shifting a graph to the right by 2 units?

Back

Every point on the graph moves 2 units to the right.

Front

What is the equation of the function that is graphed if it opens downwards and has a vertex at (0,0)?

Back

f(x) = -√x.

Front

What does the notation f(x) = -√-x indicate about the graph?

Back

It reflects the graph over the y-axis and then over the x-axis.