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.

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.

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.