Question

x f(x)
0 -2,
2 4,
6 16

What is the value of f(3)?

Answer 1

Answer:

$f(3)=7$

Step-by-step explanation:

Given:

$x$              $f(x)$

0                     -2

2                     4

6                     16

Let us first determine whether the rate of change of the function is constant or not.

The rate of change of the function is given as:

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, for $x_1=0,f(0)=-2,x_2=2,f(2)=4$

$m=\frac{4-(-2)}{2-0}=\frac{4+2}{2}=\frac{6}{2}=3$

For the next set of numbers, $x_2 = 2, f(2)=4,x_3=6,f(6)=16$

$m=\frac{16-4}{6-2}=\frac{12}{4}=3$

Therefore, the rate of change of the function is a constant. Therefore, the relationship is a linear relationship.

A linear relationship with a given point $(x_1,y_1)$ and constant rate of change $m$ is given as:

$y-y_1=m(x-x_1)\\y-(-2)=3(x-0)\\y+2=3x\\y=3x-2\\\therefore f(x)=3x-2$

Now, value of $f(3)$ is obtained by plugging in 3 for $x$ in the above expression.

$f(3)=3(3)-2\\f(3)=9-2=7$