Parent Functions and Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

What transformation occurs when f(x) is replaced with f(x) + k?

Back

A vertical translation up by k units.

Front

What transformation occurs when f(x) is replaced with f(x - h)?

Back

A horizontal translation right by h units.

Front

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

Back

It reflects the graph across the x-axis.

Front

What is the equation of a vertical stretch of a function f(x) by a factor of a?

Back

The equation is af(x).

Front

How does the graph of y = |x| change when transformed to y = |x - h|?

Back

The graph shifts horizontally to the right by h units.

Front

What does the transformation y = f(x) + k represent?

Back

A vertical translation up by k units.

Front

What is the equation for a quadratic function that opens upwards?

Back

y = ax^2 + bx + c, where a > 0.

Front

What is the effect of adding a constant outside the function, such as f(x) + c?

Back

It shifts the graph vertically.

Front

What does the transformation y = -f(x) do to the graph?

Back

It reflects the graph across the x-axis.