All Algebra II Resources
Example Questions
Example Question #2 : Graphing Absolute Value Functions
Give the vertex of the graph of the function .
None of the other choices gives the correct response.
Let
The graph of this basic absolute value function is a "V"-shaped graph with a vertex at the origin, or the point with coordinates . In terms of ,
,
or, alternatively written,
The graph of is the same as that of , after it shifts 10 units left ( ), it flips vertically (negative symbol), and it shifts up 10 units (the second ). The flip does not affect the position of the vertex, but the shifts do; the vertex of the graph of is at .
Example Question #7 : Graphing Absolute Value Functions
Which of the following absolute value functions is represented by the following graph?
The equation cannot be determined from the graph.
The equation can be determined from the graph by following the rules of transformations; the base equation is:
The graph of this base equation is:
When we compare our graph to the base equation graph, we see that it has been shifted right 3 units, up 1 unit, and our graph has been stretched vertically by a factor of 2. Following the rules of transformations, the equation for our graph is written as:
Certified Tutor
Certified Tutor