Transformations of Functions

Front

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

Back

The domain is [0, ∞).

Front

What transformation is applied to the function f(x) = √x to get g(x) = -√x?

Back

The transformation is a reflection over the x-axis.

Front

What is the equation of the graph that represents a vertical shift of f(x) = x² down by 3 units?

Back

The equation is g(x) = x² - 3.

Front

What does the transformation g(x) = |x + 2| - 3 represent?

Back

It represents a horizontal shift left by 2 units and a vertical shift down by 3 units.

Front

If f(x) = (x - 2)² - 3, what is the vertex of the parabola?

Back

The vertex is (2, -3).

Front

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

Back

It reflects the graph of the function over the x-axis.

Front

What is the range of the function f(x) = x²?

Back

The range is [0, ∞).

Front

If f(x) = |x|, what is the transformation to get g(x) = |x - 3|?

Back

The transformation is a horizontal shift right by 3 units.

Front

What is the effect of a vertical stretch on the function f(x) = x², such as g(x) = 3x²?

Back

It stretches the graph vertically by a factor of 3.

Front

What transformation is applied to f(x) = x² to get g(x) = (x + 1)²?

Back

The transformation is a horizontal shift left by 1 unit.