graph transformations and parent functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (y = x), quadratic functions (y = x^2), and absolute value functions (y = |x|).

Front

Describe the transformation: g(x) = -3√(x - 2) + 1 in terms of f(x) = √x.

Back

Reflects over the x-axis, vertical stretch by 3, right 2, up 1.

Tags

CCSS.HSF.BF.B.3

Front

What is the parent function of the absolute value function?

Back

The parent function of the absolute value function is y = |x|.

Front

What type of function is represented by the equation y = |x|?

Back

Absolute value function.

Tags

CCSS.HSF-IF.C.7D

Front

How do you shift the graph of y = |x| to the right by 5 units?

Back

The equation becomes y = |x - 5|.

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

What does a vertical stretch by a factor of 3 do to the graph of a function?

Back

It makes the graph steeper, stretching it away from the x-axis.

Front

If a function is shifted left 2 units, how is the equation modified?

Back

The equation changes from f(x) to f(x + 2).

Front

What is the transformation of the function g(x) = f(x - 2) + 5?

Back

The graph of f(x) is shifted right 2 units and up 5 units.

Front

What is the general form of a quadratic function?

Back

The general form is y = ax^2 + bx + c, where a, b, and c are constants.