Graphing techniques, Need urgent help! (1 Viewer)

[MinnieMinnie]

Hello!
I have an exam in 2 days and my teacher passed us a revision sheet for practice!


There's a question that I have !


The question is:

The function y=1/(1+x^2)has been dilated vertically and horizontally by a factor of 2 and reflected about the y-axis. THe new function is:

a. y= 8/(4+x^2)
b. y= 8/(4-x^2)
c. y= 4/(4+x^2)
d. y= 4/(4-x^2)


and the answer is a.

But I do:
y=2(1/(1+x^2)

Y=2/(2+2(-0.5x)^2)

y= 4/(2+x^2)



And that is not even an option
So yes, please help

 

[hellohi786364]

The mistake is in your second step, where you have multiplied -0.5x by 2, then squaring. The order of operations requires for the -0.5x to be squared first, as indices come before multiplication and the entire -0.5x is in parentheses, hence it is all included. Squaring -0.5x first will give y=2/(2+2(0.25)x^2), which can be simplified (by multiplying both numerator and denominator by 2) to give y = 4/(4+x^2) and then finally multiplied by two for the vertical dilation to give y = 8/(8+x^2).

y = 1/(1+x^2)
y = 2/(1+x^2) (vertical dilation)
y = 2/(1+(0.5x)^2) (horizontal dilation)
y = 2/1+(-0.5x)^2) (reflection about y-axis)
y = 2/(1+0.25x^2)
y = 8/(4+x^2)

 

[MinnieMinnie]

The mistake is in your second step, where you have multiplied -0.5x by 2, then squaring. The order of operations requires for the -0.5x to be squared first, as indices come before multiplication and the entire -0.5x is in parentheses, hence it is all included. Squaring -0.5x first will give y=2/(2+2(0.25)x^2), which can be simplified (by multiplying both numerator and denominator by 2) to give y = 4/(4+x^2) and then finally multiplied by two for the vertical dilation to give y = 8/(8+x^2).

y = 1/(1+x^2)
y = 2/(1+x^2) (vertical dilation)
y = 2/(1+(0.5x)^2) (horizontal dilation)
y = 2/1+(-0.5x)^2) (reflection about y-axis)
y = 2/(1+0.25x^2)
y = 8/(4+x^2)

Thank you!!!!
But how do you get the last line from the second last line if you could kindly explain that to me!

 

[hellohi786364]

Thank you!!!!
But how do you get the last line from the second last line if you could kindly explain that to me!

Multiplied both numerator and denominator by 4.

 

[MinnieMinnie]

Multiplied both numerator and denominator by 4.

Why do you multiply the denominator by 4??!!

 

[hellohi786364]

Just so the x^2 doesn't have 0.25 as a coefficient, just makes the function look nicer really. Can multiply both numerator and demonitator by 4 because it's really just multiplying the function by 4/4, which is one and doesn't change the function.

 

[MinnieMinnie]

Just so the x^2 doesn't have 0.25 as a coefficient, just makes the function look nicer really. Can multiply both numerator and demonitator by 4 because it's really just multiplying the function by 4/4, which is one and doesn't change the function.

Thank you so much!!! i am grateful to you!!!

 

[CM_Tutor]

You can do the transformations all at once:


Note that you can also ignore the reflection in the y-axis as the starting function is even and this will not be changed by the dilations.

 

[MinnieMinnie]

You can do the transformations all at once:


Note that you can also ignore the reflection in the y-axis as the starting function is even and this will not be changed by the dilations.

thank you!!!