Question

The function f(x) is graphed on the coordinate plane.

Answer 1

The answer is f(-2)=-2, go over -2 units and move vertically -2 units

Answer 2

Answer:

The value of f(-2) is, -2

Step-by-step explanation:

The graph which is shown on the coordinate plane passes through the two points i.e, (2,0) and (0, -1).

First find the equation for this line:

Using Point-Slope form for the equation of line: $y-y_{1}=m(x-x_{1})$  ..[1]

where m is the slope given by ;

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

First find the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-1-0}{0-2}$

⇒ $m=\frac{-1}{-2} =\frac{1}{2}$

Now, substitute the value of m=$\frac{1}{2}$ , $x_{1}$= 2and $y_{1}$=0 in equation [1];

$y-0=(\frac{1}{2})(x-2)$ or

$y=\frac{1}{2}\cdot (x-2)$

In this graph x represents the input of the process and Y the output of the process and f the function of the variable x i.e, y=f(x)

∴ $y=f(x)=\frac{1}{2}(x-2)$        ....[2]

now, we put the value of x=-2 inequation [2] to solve for f(-2).

$f(-2)=\frac{1}{2}(-2-2) =\frac{1}{2} \cdot (-4)$

Simplify we get;

$f(-2)=-2$