Question

The function f (x) is graphed on the coordinate plane what is f(-4) Enter your answer F(-4)= what

Answer 1

Given:

The objective is to find f(-4).

Step-by-step explanation:

The general equation of a straight line is,

`y=mx+b\text{ . . . . .(1)}`

Here, m represents the slope of the straight line, b represents the y-intercept.

To find m:

The value of slope can be calculated by considering two coordinates from the graph,

`\begin{gathered} (x_1,y_1)=(4,0) \\ (x_2,y_2)=(0,2) \end{gathered}`

On plugging the values in the formula of the slope,

`\begin{gathered} m=(2-0)/(0-4) \\ =(2)/(-4) \\ =-(1)/(2) \end{gathered}`

Thus, the slope of the graph is -1/2.

From the graph, the y-intercept of the graph is 2.

On plugging the obtained values in equation (1),

`y=-(1)/(2)x+2\text{ . . . . (2)}`

At x = -4 in equation (2),

`\begin{gathered} f(-2)=-(1)/(2)(-2)+2 \\ =1+2 \\ =3 \end{gathered}`

Hence, the value of f(-4) is 3.