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AleksandrR [38]
3 years ago
8

F(x) = x2 + 3x + 2 is shifted 2 units left. The result is g(x). What is g(x)?

Mathematics
1 answer:
Misha Larkins [42]3 years ago
4 0

Answer:

g(x) = x^2+7x+12

Step-by-step explanation:

If we are given a function <em>f</em> and we want to shift it <em>a</em> units horizontally, the resulting function will be f(<em>x</em> - <em>a</em>), where a positive <em>a</em> is a shift rightwards and a negative <em>a</em> is a shift leftwards.

We have the function:

f(x)=x^2+3x+2

And we want to shift it two units to the left.

Since we want to shift it two units to the left, <em>a</em> = -2. Therefore, our new function, let's call it <em>g</em>, must be f(<em>x</em> - (-2)) or f(<em>x</em> + 2). Substitute:

g(x) = f(x+2)=(x+2)^2+3(x+2)+2

Simplify. Expand:

g(x) = (x^2+4x+4)+(3x+6)+2

Combine like terms. Hence:

g(x) = x^2+7x+12

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