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Graph transformations of functions

f(x) =-x³+2x²+5x-10
g(x)=x³+2x²-5x-10
Explain how the graph of y=f(x) can be transformed into the graph of y=g(x).
please may you fully justify your answer.
Original post by Calculus123
f(x) =-x³+2x²+5x-10
g(x)=x³+2x²-5x-10
Explain how the graph of y=f(x) can be transformed into the graph of y=g(x).
please may you fully justify your answer.


What difference do you notice between the two functions?
Reply 2
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Quasar205
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The a coefficient is negative and 5x has become
-5x I'm not sure how to explain it as a transformation
Original post by RDKGames
What difference do you notice between the two functions?
Original post by Calculus123
The a coefficient is negative and 5x has become
-5x I'm not sure how to explain it as a transformation


That's not the only difference. What else?
Reply 4
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Quasar205
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I don't know please just give me a clue to start
Original post by RDKGames
That's not the only difference. What else?
Original post by Calculus123
I don't know please just give me a clue to start


The sign of x3x^3 also switches.

So every odd power term in xx swaps the sign, but every even power stays the same.

Does that help?
Reply 6
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Quasar205
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So is it some kind of reflection?
Original post by RDKGames
The sign of x3x^3 also switches.

So every odd power term in xx swaps the sign, but every even power stays the same.

Does that help?
Original post by Calculus123
So is it some kind of reflection?


Yeah it is, but you need to be more specific than that.
Reply 8
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Quasar205
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Reflection at x=0 the y-axis
Original post by Calculus123
Reflection at x=0 the y-axis


Yep.
Reply 10
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Quasar205
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Also how would you transform
f(x) =-x³+2x²+5x-10 to
h(x) =-8x³+8x²+10x-10
I know it's some kind of enlargement but not sure how to explain it
Original post by Calculus123
Also how would you transform
f(x) =-x³+2x²+5x-10 to
h(x) =-8x³+8x²+10x-10
I know it's some kind of enlargement but not sure how to explain it


It’s not enlargement.

You should really first identify “what do I need to replace x by in f(x) in order to obtain h(x)?”

In the first question, it’s not hard to see that you replace x with (-x) hence the reflection in the y-axis.
So what’s the replacement here??
Reply 12
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Quasar205
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But it is an enlargement of scale factor 1/2.
Original post by RDKGames
It’s not enlargement.

You should really first identify “what do I need to replace x by in f(x) in order to obtain h(x)?”

In the first question, it’s not hard to see that you replace x with (-x) hence the reflection in the y-axis.
So what’s the replacement here??
Original post by Calculus123
But it is an enlargement of scale factor 1/2.


It's not.

It's a stretch in only one direction.

An enlargement would be *two* equal stretches in perpendicular directions.
Reply 14
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Quasar205
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So is it a stretch of scale factor 1/2 in the x-direction.
Original post by Calculus123
So is it a stretch of scale factor 1/2 in the x-direction.


Yes.

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