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How do you write on equation for a function, g(x), that has been translated 3 units to the right of #f(x)=2x^2-8x+1#?

Answer 1

Benjamin Achtenberg

See explanation.

If you transfer a graph of #f(x)# by moving it 3 units to the right, you get the graph of #g(x)=f(x-3)#. Here you get:

#g(x)=f(x-3)=2(x-3)^2-8(x-3)+1#

#g(x)=2*(x^2-6x+9)-8x+24+1#

#g(x)=2x^2-12x+18-8x+25#

#g(x)=2x^2-20x+43#

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Answer 2

Lily Anderson

To write an equation for the function g(x) that has been translated 3 units to the right of f(x) = 2x^2 - 8x + 1, we use the transformation rules for functions.

The transformation of moving a function to the right by 'a' units is represented as f(x - a). Therefore, to move f(x) three units to the right, we replace x with (x - 3) in the equation.

So, the equation for g(x), the translated function, is: g(x) = 2(x - 3)^2 - 8(x - 3) + 1

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.