Square root functions

Front

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

Back

[0, infinity)

Front

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

Back

[0, infinity)

Front

What is the parent function of square root functions?

Back

f(x) = √x

Front

What transformation occurs when the function f(x) = √x is shifted left by 2 units?

Back

The new function is f(x) = √(x + 2).

Front

What transformation occurs when the function f(x) = √x is reflected over the x-axis?

Back

The new function is f(x) = -√x.

Front

What is the effect of adding a constant to the square root function, such as f(x) = √x + 2?

Back

It shifts the graph of the function up by 2 units.

Front

What is the effect of subtracting a constant from the square root function, such as f(x) = √x - 2?

Back

It shifts the graph of the function down by 2 units.

Front

What is the effect of multiplying the square root function by a negative number, such as f(x) = -√x?

Back

It reflects the graph over the x-axis.

Front

What is the effect of multiplying the square root function by a positive number, such as f(x) = 2√x?

Back

It vertically stretches the graph by a factor of 2.

Front

What is the general form of a transformed square root function?

Back

f(x) = a√(x - h) + k, where (h, k) is the vertex.