Video Transcript
Which of the following set of
coordinates lies on 𝑓 of 𝑥 is equal to negative 19𝑥 minus 16? Is it (A) 10, negative 16; (B) 10,
negative 206; (C) negative 206, 10; or (D) negative 206, negative 16?
We are used to any pair of
coordinates being written in the form 𝑥, 𝑦. The first coordinate is the
𝑥-value, and the second is the 𝑦-value. The function 𝑓 of 𝑥 is equal to
negative 19𝑥 minus 16 is the same as 𝑦 equals negative 19𝑥 minus 16. As 𝑦 and 𝑓 of 𝑥 are
interchangeable, we can write the coordinate pair as 𝑥, 𝑓 of 𝑥. The first value is known as the
input and the second value the output.
We need to work out which of the
four options satisfies the function. We notice that both option (A) and
option (B) have an input or 𝑥-value of 10. This means that in order to
calculate the output, we need to work out 𝑓 of 10. Substituting in 𝑥 equals 10 gives
us negative 19 multiplied by 10 minus 16. Multiplying a negative number by a
positive gives a negative answer. So negative 19 multiplied by 10 is
negative 190. Subtracting 16 from this gives us
negative 206. This means that the coordinate pair
10, negative 206 lies on the function. As option (A) was 10, negative 16,
this is incorrect. Option (B), on the other hand, was
10, negative 206. So this is the correct answer.
We could check to see if options
(C) and (D) are correct by substituting negative 206 in for 𝑥. 𝑓 of negative 206 is equal to
negative 19 multiplied by negative 206 minus 16. We can clearly see that this will
not satisfy either of our options, as our value is too large. An input of negative 206 gives an
output of 3898. The coordinate pair negative 206,
3898 lies on the function. This does not correspond to option
(C) or (D). So these are both incorrect. The correct answer is option
(B).
