Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x + 7|? 7 units up 7 units down
2 answers:
Answer: The correct option is
(C) 7 units left.
Step-by-step explanation: We are given to select the correct description of the translation of graph y = |x| to obtain the graph of y = |x + 7|.
We know that
if the parent absolute function y = |x| is shifted a units to the left, then the new function is written as
The given translated function is y = |x + 7|.
It describes that the function y = |x| is shifted 7 units to the left.
Thus, the correct description is
7 units left.
Option (C) is CORRECT.
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Answer:
The given relation R is equivalence relation.
Step-by-step explanation:
Given that:
Where is the relation on the set of ordered pairs of positive integers.
To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.
1. First of all, let us check reflexive property:
Reflexive property means:
Here we need to prove:
As per the given relation:
which is true.
R is reflexive.
2. Now, let us check symmetric property:
Symmetric property means:
Here we need to prove:
As per the given relation:
means
means
Hence true.
R is symmetric.
3. R to be transitive, we need to prove:
means
.... (1)
means
...... (2)
To prove:
To be we need to prove:
Multiply (1) with (2):
So, R is transitive as well.
Hence proved that R is an equivalence relation.