Parent Functions and Transformations

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, quadratic, cubic, and absolute value functions.

Front

What transformation does the function m(x) = f(x + 1) represent?

Back

Left 1 Unit

Front

What are the zeros of a function?

Back

The zeros of a function are the values of x for which the function equals zero (f(x) = 0).

Front

Which function represents a translation of 2 units right and a vertical stretch by a factor of 5?

Back

f(x) = 5(x - 2)²

Front

How do you shift the quadratic function f(x) = x² up 3 units and to the right 4 units?

Back

f(x) = (x - 4)² + 3

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does a vertical stretch by a factor of k do to a function?

Back

A vertical stretch by a factor of k multiplies the output of the function by k, making it steeper if k > 1.

Front

What is the effect of a horizontal translation of a function?

Back

A horizontal translation shifts the graph of the function left or right along the x-axis.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

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

Back

It shifts the graph of the function down by k units.