Transformations of Parent Functions

Front

What is the parent function for quadratic equations?

Back

f(x) = x^2

Front

Describe the transformation of the function g(x) = 5x^2 + 2 from its parent function f(x) = x^2.

Back

Vertical stretch by a factor of 5 and a vertical shift upward by 2 units.

Front

What is the parent function for cubic equations?

Back

f(x) = x^3

Front

How does the graph of f(x) = -x^2 reflect the parent function f(x) = x^2?

Back

It reflects over the x-axis.

Front

What does a vertical shift of 'k' units mean in the function g(x) = f(x) + k?

Back

The graph of f(x) is shifted vertically by 'k' units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

What transformation is represented by the function g(x) = f(x - h)?

Back

A horizontal shift to the right by 'h' units if h is positive, and to the left if h is negative.

Front

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

Back

It reflects the graph over the x-axis.

Front

Describe the transformation of the function g(x) = |x| - 1 from its parent function f(x) = |x|.

Back

A vertical shift downward by 1 unit.

Front

What does the notation I x I represent in transformations?

Back

It represents the absolute value function, which reflects negative values of x to positive.

Front

How do you describe a transformation that moves a graph right 3 units and down 4 units?

Back

The transformation can be represented as g(x) = f(x - 3) - 4.