### Video Transcript

This is the graph of 𝑦 equals 𝑔
of 𝑥. Which of the following is 𝑔 of
negative 𝑥? Is it graph A, graph B, or graph
C?

We begin by recalling that the
graph of 𝑔 of negative 𝑥 will be a reflection in the 𝑦-axis of the graph of 𝑔 of
𝑥. We can see from the graph of 𝑔 of
𝑥 that this function has roots at 𝑥 equals negative three and 𝑥 equals two. We know that when we reflect a
function in the 𝑦-axis, the roots change sign. This means that the roots of 𝑔 of
negative 𝑥 will be 𝑥 equals negative two and 𝑥 equals three. We can therefore eliminate option
(A). And in fact, this is a reflection
of 𝑔 of 𝑥 in the 𝑥-axis. The function 𝑔 of 𝑥 has a
𝑦-intercept approximately equal to 1.2. When reflecting any function in the
𝑦-axis, the 𝑦-intercept remains unchanged. This means that we can also
eliminate option (C).

The correct answer is therefore
option (B). This is the graph of the function
𝑔 of negative 𝑥 as the 𝑦-intercept has remained unchanged and the roots have
changed sign.