Question

Select all the functions whose graphs include the point $(16,4)$.

• A. $\mathrm{y}=2\mathrm{x}$
• B. $\mathrm{y}={\mathrm{x}}^2$
• C. $\mathrm{y}=\mathrm{x}+12$
• D. $\mathrm{y}=\mathrm{x}-12$
• E. $\mathrm{y}=14\mathrm{x}$

Answer 1

The correct option is D

$\mathrm{y}=\mathrm{x}-12$

Step-1: Explanation for correct answer:

The functions whose graphs include the point $(16,4)$, will also satisfy the point $(16,4)$.

For option (D): $\mathrm{y}=\mathrm{x}-12$

Substitute $\mathrm{y}=4,\mathrm{x}=16$

Thus, $4=16-12$

$\Rightarrow$ $4=4$

So option $D$ is not correct

Step-2: Explanation for incorrect answer:

For option $\left(A\right)$: $\mathrm{y}=2\mathrm{x}$

Substitute $\mathrm{y}=4,\mathrm{x}=16$

Thus, $4=2\left(16\right)$

So option $A$ is not correct

For option $\left(B\right)$: $\mathrm{y}={\mathrm{x}}^2$

Substitute $\mathrm{y}=4,\mathrm{x}=16$

Thus, $4={\left(16\right)}^2$

$\Rightarrow$ $4=256$,

So option $B$ is not correct

For option $\left(C\right)$: $\mathrm{y}=\mathrm{x}+12$

Substitute $\mathrm{y}=4,\mathrm{x}=16$

Thus, $4=16+12$

$\Rightarrow$ $4=28$

So option $C$ is not correct

For option (E): $\mathrm{y}=14\mathrm{x}$

Substitute $\mathrm{y}=4,\mathrm{x}=16$

Thus, $4=14\left(16\right)$

$\Rightarrow$ $4=224$

So option $E$ is not correct

Hence, the correct option is $\left(D\right)$.