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Charra [1.4K]
3 years ago
13

Given the function f(x) = x3 + x2 − 2x + 1, what is the resulting function when f(x) is shifted to the left 1 unit?

Mathematics
2 answers:
Mekhanik [1.2K]3 years ago
8 0
The answer is B.

Explanation:

If c is a positive real number, then the graph of
f(x – c) is the graph of y = f(x) shifted to the right
c units.
Horizontal Shifts
If c is a positive real
number, then the
graph of f(x + c) is
the graph of y = f(x)
shifted to the left
alekssr [168]3 years ago
8 0

Answer:

Option B is correct

Step-by-step explanation:

Given: f(x)=x^3+x^2-2x+1

If a graph f(x) is shifted a units to the left then it becomes f(x+a)

Here, the graph is shifted 1 unit to the left . On taking a=1, we get graph f(x+1)

Using formula \left ( a+b \right )^{3}=a^3+b^3+3a^2b+3ab^2 , we get

\left ( x+1 \right )^{3}=x^3+1+3x^2+3x

Using formula (a+b)^{2}=a^2+b^2+2ab , we get

\left ( x+1 \right )^{2}=x^2+1+2x

Using distributive property over multiplication i.e a\left ( b+c \right )=ab+ac , we get

2\left ( x+1 \right )=2x+2

Therefore,

f(x)=x^3+x^2-2x+1\\\Rightarrow f\left ( x+1 \right )=\left ( x+1 \right )^{3}+\left ( x+1 \right )^{2}-2\left ( x+1 \right )+1\\=x^3+1+3x^2+3x+x^2+2x+1-2x-2+1\\=x^3+4x^2+3x+1

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