Parent Functions and Transformations - Algebra

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 effect does an a-value greater than 1 have on the graph of a function?

Back

It makes the graph skinnier.

Front

What effect does an a-value between 0 and 1 have on the graph of a function?

Back

It makes the graph wider.

Front

What does a positive k-value do to the graph of a function?

Back

It shifts the graph upward by k units.

Front

What does a negative k-value do to the graph of a function?

Back

It shifts the graph downward by k units.

Front

How do you represent a horizontal shift to the left in a function?

Back

By adding a positive value inside the function's argument, e.g., f(x) = (x + h)^2 for a shift left by h units.

Front

How do you represent a horizontal shift to the right in a function?

Back

By subtracting a positive value inside the function's argument, e.g., f(x) = (x - h)^2 for a shift right by h units.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What does the term 'transformation' refer to in algebra?

Back

Transformation refers to changes made to the graph of a function, including shifts, stretches, compressions, and reflections.

Front

What is the effect of a negative a-value on the graph of a function?

Back

It reflects the graph across the x-axis.