PS Transformation of Functions

Front

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

Back

[0,∞) - The range of a quadratic function that opens upwards is from 0 to infinity.

Front

Describe the transformation from the parent graph f(x) = x^2 to g(x) = -f(x) + 4.

Back

Reflect over x-axis and shift up 4 units.

Front

Which equation represents a quadratic function translated left 4 units?

Back

y = (x + 4)^2 - A left translation is indicated by adding to x in the function.

Front

If f(x) = x^2, what is the effect of the equation g(x) = f(x) - 5?

Back

The graph of g(x) is the graph of f(x) shifted down 5 units.

Front

Match the equation y = (x - 2)^2 + 4 with its graph.

Back

The vertex of the graph is at (2, 4) and it opens upwards.

Front

What does it mean to reflect a graph over the x-axis?

Back

The y-values of the function are multiplied by -1, flipping the graph upside down.

Front

What is the vertex form of a quadratic function?

Back

y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How does the value of 'a' in the vertex form affect the graph?

Back

If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What is the effect of translating a graph right 3 units?

Back

Replace x with (x - 3) in the function.

Front

What is the effect of translating a graph down 4 units?

Back

Subtract 4 from the entire function.