Question

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

A f(x − 1) = x3 − 2x2 − x + 3
B f(x + 1) = x3 + 4x2 + 3x + 1
C f(x) − 1 = x3 + x2 − 2x
D f(x) + 1 = x3 + x2 − 2x + 2

Answer 1

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`

Answer 2

The answer is B.

Step-by-step 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