Question

Analyze the given information and find the output when input is 4.


The output is .

• A. 40
• B. 30
• C. 60
• D. 50

Answer 1

The correct option is A 40


For each input value, there is only one value of y.
So, the graph represents a function.

From the graph, we observe:


The first difference are not same, so the function can't be linear.

The nature of function can be found by finding the differences between successive first differences, which are called second differences. Here, as the second differences are all equal, the function is quadratic.


$\text{Since, the second difference all are + 5,}$
$\text{so, the function is quadratic}$
$i.e,y=a{x}^2$

Let us consider one point, say (2,10) and substitute in the above equation:

$y=a{x}^2$

$\Rightarrow 10=a\left(2^2\right)$

$\Rightarrow 10=a\times 4$

$\Rightarrow \frac{10}{4}=a$

$\Rightarrow a=2.5$

$\Rightarrow \text{So,}y=2.5x^2$

$\text{So, at input x = 4, output y =}2.5(4{)}^2=40$

∴ The output is 40.