Question

The given graph can be represented by which of the following functions?

• A. $y=x^3-2x^2+3x$
• B. $y=x^3+2x^2-3x$
• C. $y=x^3-2x^2-3x$
• D. $y=x^3+2x^2+3x$

Answer 1

Answer: (C)

$y=x^3-2x^2-3x$

From the graph consider the point $(-1,0)$. That is, when $x=-1,y=0$.
Now let us check which of the given functions satisfy the above condition.
A. $y=x^3-2x^2+3x$
Substitute $x=-1$, we get $y=(-1{)}^3-2(-1{)}^2+3(-1)=-1-2-3=-6$
Thus $x=-1$ yields $y=-6$
Therefore we reject A.
B. $y=x^3+2x^2-3x$
Substitute $x=-1$, we get $y=(-1{)}^3+2(-1{)}^2-3(-1)=-1+2+3=4$
Thus $x=-1$ yields $y=4$
Therefore we reject B.
C. $y=x^3-2x^2-3x$
Substitute $x=-1$, we get $y=(-1{)}^3-2(-1{)}^2-3(-1)=-1-2+3=0$
Thus $x=-1$ yields $y=0$
Therefore we consider C for now.
D. $y=x^3+2x^2+3x$
Substitute $x=-1$, we get $y=(-1{)}^3+2(-1{)}^2+3(-1)=-1+2-3=-2$
Thus $x=-1$ yields $y=-2$
Therefore we reject D.
Hence C is the only option that satisfies the point from the graph.
Therefore we conclude that the given graph represents function $y=x^3-2x^2-3x$