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Translations of graphs need help

Can someone reflect these in the y-axis please?

y=2x^3+x^2-5x+1

y=3sin(x)

And can someone stretch these parallel to the x axis please

y=x^2 by scale factor 3 parallel to the x-axis

y=x^2-4x+1 by scale factor 0.5 parallel to the x axis

y=3sin(x) by scale factor 1/5 parallel to the x-axis

45 minutes ago
- 4 days left to answer.
Reply 1
A reflection in the y axis is to swap around the positive and negative sides of the x axis.

To stretch f(x) by a factor of a along the x axis, you need f(x) to come at a*x, hence you get the stretch being f(x/a). The division by a means x has to be a times as large to get the same value of f.
Reply 2
agree to that ^^^^^
Reply 3
Original post by iceman95
Can someone reflect these in the y-axis please?

y=2x^3+x^2-5x+1

y=3sin(x)

And can someone stretch these parallel to the x axis please

y=x^2 by scale factor 3 parallel to the x-axis

y=x^2-4x+1 by scale factor 0.5 parallel to the x axis

y=3sin(x) by scale factor 1/5 parallel to the x-axis

45 minutes ago
- 4 days left to answer.


Generally:
let y=f(x)y=f(x)
THen
Reflection in the y-axis: y=f(x)y=f(-x)
Reflection in the x-axis:y=f(x)y=-f(x)
Translating by 'a' parallel to the x: y=f(xa)y=f(x-a)
Translating by 'a' parallel to the y: y=f(x)+ay=f(x)+a
Streching by scale factor 'a' parallel to x: y=f(1ax)y=f(\frac{1}{a}x)
Streching by scale factor 'a' parallel to y: y=af(x)y=a\cdot f(x)

F.e for 2nd
y=sin3xy=sin(3x)=sin3xy=sin3x \rightarrow y=sin(-3x)=-sin3x
for 4th
Unparseable latex formula:

y=x^2-4x+1 \rightarrow y=\left (2x)^2-4(2x)+1=4x^2-8x+1

Reply 4
Original post by ztibor
Generally:
let y=f(x)y=f(x)
THen
Reflection in the y-axis: y=f(x)y=f(-x)
Reflection in the x-axis:y=f(x)y=-f(x)
Translating by 'a' parallel to the x: y=f(xa)y=f(x-a)
Translating by 'a' parallel to the y: y=f(x)+ay=f(x)+a
Streching by scale factor 'a' parallel to x: y=f(1ax)y=f(\frac{1}{a}x)
Streching by scale factor 'a' parallel to y: y=af(x)y=a\cdot f(x)

F.e for 2nd
y=sin3xy=sin(3x)=sin3xy=sin3x \rightarrow y=sin(-3x)=-sin3x
for 4th
Unparseable latex formula:

y=x^2-4x+1 \rightarrow y=\left (2x)^2-4(2x)+1=4x^2-8x+1



How can I reflect y=2x^3+x^2-5x+1 into the y-axis?

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