Question

$y=x^3+2x^2–3x+1$

Students A and B are asked about the dependent and the independent variables of the above function.

A: Dependent$\to x,$ Independent $\to y$
B: Dependent $\to y,$ Independent $\to x$

Choose the correct option.

Answer 1

A variable that depends on the value of another number is called a dependent variable.

A variable that is independent of changes is called an independent variable.

Consider the given equation $y=x^3+2x^2–3x+1.$

Let us put $x=1$ in the equation.
$⟹y=1^3+2(1{)}^2–3(1)+1$
$=1+2–3+1$
​​​​​​​$=1$

If we put $x=2$ in the equation, we get:
​​​​​​​$y=2^3+2(2{)}^2–3(2)+1$
​​​​​​​$=8+8–6+1$
​​​​​​​$=11$

Thus, the value of $y$ depends on the value of $x.$

​​​​​​​Hence, $x$ is the independent variable and $y$ is the dependent variable.

​​​​​​​Thus, only B is correct.