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All Algebra II Resources
Refer to the above figure.
Which of the following functions is graphed?
Correct answer:
Explanation:
Below is the graph of :
The given graph is the graph of reflected in the -axis, then translated up 6 units. This graph is
The function graphed is therefore
Refer to the above figure.
Which of the following functions is graphed?
Correct answer:
Explanation:
Below is the graph of :
The given graph is the graph of reflected in the -axis, then translated left 2 units (or, equivalently, right units. This graph is
, where .
The function graphed is therefore
Refer to the above figure.
Which of the following functions is graphed?
Possible Answers:
The correct answer is not given among the other responses.
Correct answer:
Explanation:
Below is the graph of :
The given graph is the graph of translated by moving the graph 7 units left (that is, unit right) and 2 units down (that is, units up)
The function graphed is therefore
where . That is,
What is the equation of the above function?
Correct answer:
Give the vertex of the graph of the function .
Possible Answers:
None of the other choices gives the correct response.
Correct answer:
Explanation:
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 ,
The graph of this function can be formed by shifting the graph of left 6 units ( ) and down 7 units (). The vertex is therefore located at .
Give the vertex of the graph of the function .
Possible Answers:
None of the other choices gives the correct response.
Correct answer:
Explanation:
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 .
Which of the following absolute value functions is represented by the following graph?
Possible Answers:
The equation cannot be determined from the graph.
Correct answer:
Explanation:
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: