Question

the function v (graphed below in blue) is a transformation of function h (graphed in black). what is the formula for function v in terms of h? draw (graph omitted) options: h(x)+2, h(x)-2, h(x+2), h(x-2)

Explanation:

Step1: Analyze Vertical Shift

Check the y - intercepts. The black graph (h) has a y - intercept of 4, and the blue graph (v) has a y - intercept of 2. The difference is \(4 - 2=2\), so v is h shifted down by 2 units.

Step2: Determine the Transformation

A vertical shift down by 2 units for a function \(y = h(x)\) gives \(y=h(x)-2\). We can also check other points. For example, the vertex of h is at \((- 4,0)\) and the vertex of v is at \((-4,-2)\), which is a vertical shift down by 2.

Answer:

\(h(x)-2\) (corresponding to the option \(h(x)-2\))