Polynomial Transformations

Front

What is a polynomial transformation?

Back

A polynomial transformation refers to the process of altering the graph of a polynomial function through shifts, stretches, compressions, or reflections.

Front

How does the graph of f(x) = |x| change to g(x) = |x + 3| + 2?

Back

The graph shifts 3 units left and 2 units up.

Front

What is the effect of adding a constant to a polynomial function?

Back

Adding a constant shifts the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

What does it mean to shift a graph 5 units up?

Back

It means every point on the graph of the function is moved vertically upwards by 5 units.

Front

How does the equation y = (x + 4)² + 3 change when shifted 5 units up?

Back

The new equation is y = (x + 4)² + 8.

Front

What transformation occurs when changing f(x) = x² to g(x) = x² + 6?

Back

This represents a translation shifting the graph 6 units up.

Front

What does the transformation g(x) = (x + 9)² indicate about the graph of f(x) = x²?

Back

The graph is shifted left by 9 units.

Front

What is the effect of subtracting a number from x in a polynomial function?

Back

Subtracting a number from x shifts the graph horizontally to the right.

Front

How does the graph of f(x) = x³ change to g(x) = (x - 1)³?

Back

The graph shifts right by 1 unit.

Front

What is the impact of multiplying a polynomial function by a negative number?

Back

It reflects the graph across the x-axis.