### Home > INT3 > Chapter 9 > Lesson 9.2.3 > Problem9-124

9-124.

Ceirin’s teacher has promised a quiz for the next day, so Ceirin calls Adel to review what they had done in class. “Suppose I have $y = \text{sin}\left(2x\right)$,” says Ceirin, “what will its graph look like?”

“It will be horizontally compressed by a factor of $2$,” replies Adel, “so the period must be $π$.”

“Okay, now let’s say I want to shift it $1$ unit to the right. Do I just subtract $1$ from $x$, like always?”

“I think so,” says Adel, “but let’s check on the graphing calculator.” They proceeded to check on their calculators. After a few moments they both speak at the same time.

“Rats,” says Ceirin, “it isn’t right.”

$y = \text{sin}\left(2x – 1\right)$, while the other had $y = \text{sin}2\left(x – 1\right)$.
Which equation is correct? Had they both subtracted $1$ from $x$? Explain. Describe the rule for shifting a graph $1$ unit to the right in a way that avoids this confusion.
If you want to subtract $1$ from $x$ before multiplying, are parenthesis necessary?
The equation $y = \text{sin}2\left(x – 1\right)$ is correct. To shift the graph one unit to the right, subtract $1$ from $x$ before multiplying by anything.