Question Video: Reflecting Graphs in the Coordinate Axes Mathematics

This is the graph of 𝑦 = 𝑔(𝑥). Which of the following is 𝑔(−𝑥)? [A] Graph A [B] Graph B [C] Graph C

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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.

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