9 - 124. ceirins teacher has promised a quiz for the next day, so ceirin calls adel to review what they had…

9 - 124. ceirins 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 = sin(2x),” 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 lets 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 lets check on the graphing calculator.” they proceed to check on their calculators. after a few moments they both speak at the same time. “rats,” says ceirin, “it isnt right.” “cool,” says adel, “it works.” when they arrive at school the next morning, they compare the equations they had put into their graphing calculators while they talked on the phone. one has y = sin(2x - 1), while the other had y = sin2(x - 1). 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. homework help >

9 - 124. ceirins 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 = sin(2x),” 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 lets 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 lets check on the graphing calculator.” they proceed to check on their calculators. after a few moments they both speak at the same time. “rats,” says ceirin, “it isnt right.” “cool,” says adel, “it works.” when they arrive at school the next morning, they compare the equations they had put into their graphing calculators while they talked on the phone. one has y = sin(2x - 1), while the other had y = sin2(x - 1). 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. homework help >

Answer

Explanation:

Step1: Recall transformation rule

For a function $y = f(x)$, shifting it $h$ units to the right gives $y=f(x - h)$. For the function $y=\sin(2x)$, to shift it 1 unit to the right, we need to replace $x$ with $(x - 1)$ in the argument of the sine - function.

Step2: Analyze the two equations

The function $y=\sin(2x - 1)=\sin(2(x-\frac{1}{2}))$ is a horizontal shift of $\frac{1}{2}$ unit to the right of $y = \sin(2x)$. The function $y=\sin2(x - 1)$ is a horizontal shift of 1 unit to the right of $y=\sin(2x)$.

Step3: Determine the correct equation

The correct equation for shifting $y = \sin(2x)$ 1 unit to the right is $y=\sin2(x - 1)$. They did not both subtract 1 from $x$ in the same way. In $y=\sin(2x - 1)$, 1 is subtracted from $2x$, while in $y=\sin2(x - 1)$, 1 is subtracted from $x$ first and then the result is multiplied by 2.

Step4: State the general rule

To shift a graph of $y = f(bx)$ $h$ units to the right, the correct form is $y=f(b(x - h))$. This ensures that the entire input to the function $f$ is adjusted for the horizontal shift.

Answer:

The correct equation for shifting $y=\sin(2x)$ 1 unit to the right is $y = \sin2(x - 1)$. They did not both subtract 1 from $x$ in the same way. The rule for shifting a graph of $y = f(bx)$ $h$ units to the right is $y=f(b(x - h))$.