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

Identify the parent function of the equation y = x^2.

Back

The parent function is the quadratic function, represented as y = x^2.

Front

What transformation occurs in the function y = (x - 3)^2?

Back

The graph is translated right 3 units.

Front

What is the effect of adding a constant to a quadratic function, such as y = x^2 + 5?

Back

It translates the graph vertically upwards by 5 units.

Front

What is the parent function for exponential growth?

Back

The parent function for exponential growth is y = 2^x.

Front

How does the graph of y = -x^2 differ from y = x^2?

Back

The graph of y = -x^2 is a reflection of y = x^2 across the x-axis.

Front

What type of function is represented by y = √x?

Back

It is a square root function.

Front

What transformation is represented by the function f(x) = (x + 2)^2 - 1?

Back

The graph is translated left 2 units and down 1 unit.

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.

Front

What does the 'a' value in a quadratic function affect?

Back

The 'a' value affects the width and direction of the parabola (opening upwards if a > 0, downwards if a < 0).