Transformations of square roots

Front

What is a transformation of a function?

Back

A transformation of a function refers to a change in its position, size, or shape on a graph, which can include translations, reflections, stretches, and compressions.

Front

What is the parent function of square roots?

Back

The parent function of square roots is f(x) = √x, which is the simplest form of a square root function.

Front

What does it mean to shift a function left or right?

Back

Shifting a function left or right involves adding or subtracting a value from the input (x) of the function. For example, f(x + 2) shifts the graph left by 2 units, while f(x - 2) shifts it right by 2 units.

Front

What does it mean to shift a function up or down?

Back

Shifting a function up or down involves adding or subtracting a value from the output (f(x)) of the function. For example, f(x) + 2 shifts the graph up by 2 units, while f(x) - 2 shifts it down by 2 units.

Front

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

Back

Reflecting a function over the x-axis changes the sign of the output values. For example, if f(x) is reflected over the x-axis, the new function is -f(x).

Front

What is the effect of reflecting a function over the y-axis?

Back

Reflecting a function over the y-axis changes the sign of the input values. For example, if f(x) is reflected over the y-axis, the new function is f(-x).

Front

How does the transformation g(x) = f(x) - 4 affect the graph of f(x)?

Back

The transformation g(x) = f(x) - 4 translates the graph of f(x) downward by 4 units.

Front

What does the transformation f(x) = -√(x) indicate?

Back

The transformation f(x) = -√(x) reflects the parent square root function over the x-axis.

Front

What is the result of the transformation f(x) = -√(x) - 2?

Back

The transformation f(x) = -√(x) - 2 reflects the parent function over the x-axis and then shifts it down by 2 units.

Front

What is the solution to the equation 6(5x - 3) + 2 = 14?

Back

The solution to the equation is x = 1.