Video Transcript
Which of the following relations
does the point negative five, two not satisfy? Is it (A) 𝑓 of 𝑥 is equal to
negative 18 minus four 𝑥? (B) 𝑓 of 𝑥 is equal to negative
23 minus five 𝑥. (C) 𝑓 of 𝑥 is equal to 17 plus
three 𝑥. (D) 𝑓 of 𝑥 is equal to negative
five 𝑥 over two. Or (E) 𝑓 of 𝑥 is equal to
negative 19 plus five 𝑥 over three.
In order to answer this question,
we will substitute our value of 𝑥 into the five functions. In option (A), when 𝑥 is equal to
negative five, 𝑓 of negative five is equal to negative 18 minus four multiplied by
negative five. This simplifies to negative 18 plus
20, which is equal to two. When 𝑥 is equal to negative five,
the value of 𝑓 of 𝑥 or 𝑦 is equal to two. This means that the point negative
five, two does satisfy the relation 𝑓 of 𝑥 is equal to negative 18 minus four
𝑥. As we want the relation that the
point does not satisfy, option (A) is not correct.
Repeating this process for option
(B), we have 𝑓 of negative five is equal to negative 23 minus five multiplied by
negative five. This simplifies to negative 23 plus
25, which once again is equal to two. So option (B) is not the correct
answer.
The relation in option (C) states
that 𝑓 of 𝑥 is equal to 17 plus three 𝑥. So 𝑓 of negative five is equal to
17 plus three multiplied by negative five. This is equal to 17 minus 15, which
once again equals two. The point negative five, two does
satisfy the relation in option (C). So this is not the correct
answer.
In option (D), 𝑓 of negative five
is equal to negative five multiplied by negative five all divided by two. This is equal to 25 over two, which
is equal to 12 and a half, or 12.5. This is not equal to two. So the point negative five, two
does not satisfy the relation 𝑓 of 𝑥 is equal to negative five 𝑥 over two. Option (D) is the correct
answer.
Before finishing the question, it
is worth checking that the point does satisfy the relation in option (E). We have 𝑓 of negative five is
equal to negative 19 plus five multiplied by negative five all divided by three. Since five multiplied by negative
five is negative 25, this simplifies to negative negative six over three. This is the same as six divided by
three, which is equal to two.
We can therefore conclude that the
point negative five, two does satisfy the relations in option (A), (B), (C), and
(E). And the correct answer is therefore
option (D) 𝑓 of 𝑥 is equal to negative five 𝑥 over two. The point negative five, two does
not satisfy this relation.
