Reflections and Dilations of Parent Functions

A vertical shrink occurs when the output of a function is multiplied by a factor less than 1, causing the graph to be compressed towards the x-axis.

It translates the graph vertically by k units. If k is positive, the graph moves up; if k is negative, it moves down.

It translates the graph horizontally. If h is positive, the graph moves to the right; if h is negative, it moves to the left.

A vertical stretch occurs when the output of a function is multiplied by a factor greater than 1, causing the graph to be pulled away from the x-axis.

A reflection over the x-axis inverts the graph, changing the sign of the output values.

The general form of a quadratic function is $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants.

The parameter 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

A horizontal shift moves the graph left or right without changing its shape. It is determined by the value of h in $$f(x-h)$$ .

A vertical shift moves the graph up or down without changing its shape. It is determined by the value of k in $$f(x) + k$$ .

$$y = -|x|$$ .