Function Transformations

Front

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

Back

All real numbers.

Front

What is the parent function of a quadratic function?

Back

Quadratic function.

Front

Describe the transformation of f(x) when compared to the parent function for f(x) = (x + 7)^2.

Back

Horizontal shift left 7 units.

Front

If f(x) = x^2, what is the transformation for g(x) = (x - 3)^2?

Back

Horizontal shift right 3 units.

Front

What does the transformation f(x + 5) + 3 represent?

Back

Horizontal shift left 5 units and vertical shift up 3 units.

Front

What is the effect of a negative sign in front of the function, such as in f(x) = -x^2?

Back

Reflection over the x-axis.

Front

What is the effect of multiplying a function by a factor greater than 1, such as in f(x) = 2x^2?

Back

Vertical stretch by a factor of 2.

Front

What is the effect of multiplying a function by a factor between 0 and 1, such as in f(x) = 0.5x^2?

Back

Vertical compression by a factor of 0.5.

Front

What is the transformation for f(x) = x^2 + 4?

Back

Vertical shift up 4 units.

Front

What is the transformation for f(x) = (x - 2)^2 - 3?

Back

Horizontal shift right 2 units and vertical shift down 3 units.