Video Transcript
In which of the following intervals
is 𝑓 of 𝑥 equal to negative eight negative? Is it (A) the open interval from
negative ∞ to eight? (B) The open interval from negative
eight to ∞. (C) The open interval from negative
eight to eight. (D) The open interval from eight to
∞. Or (E) the open interval from
negative ∞ to ∞.
Let’s begin by considering what the
function 𝑓 of 𝑥 equals negative eight looks like. If we consider the normal
coordinate axes, our horizontal axis is the 𝑥-axis and our vertical one is the
𝑦-axis. The 𝑦-axis can be replaced in this
case with 𝑓 of 𝑥. We are told that 𝑓 of 𝑥 is equal
to negative eight. Therefore, we need to find negative
eight on the 𝑦- or 𝑓 of 𝑥 axis. Our function is a horizontal line
through this point. This line will continue
indefinitely to the left and to the right. As the line is entirely below the
𝑥-axis, it will always be negative. As 𝑓 of 𝑥 equal to negative eight
is always negative, the correct answer is option (E) the open interval negative ∞ to
∞. If any function is equal to a
constant, it will always just have one sign. In this case, the function is
always negative.
