Question

7. The graph of which function is shown A. f(x) = 3x + 8B. f(x) = 3x - 8C. f(x )= 8x + 3 D. f(x) = 8x - 3

Answer 1

ANSWER

B. f(x) = 3x - 8

EXPLANATION

We have the graph of a straight line given and we need to find the function that it represents.

A linear function is generally given as:

f(x) = mx + c

where m = slope

c = y intercept

So, we need to identify the slope and y intercept.

The y intercept is the point where the graph touches the y axis. From the graph, the y intercept is:

c = -8

Now, to find the slope, we use the formula:

$m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}$

where (x1, y1) and (x2, y2) are two points that lie on the graph.

Let us use the given points:

(0, -8) and (1, -5)

Therefore:

$\begin{gathered} m\text{ = }\frac{-5\text{ - (-8)}}{1\text{ - 0}}\text{ = }\frac{-5\text{ + 8}}{1} \\ m\text{ = 3} \end{gathered}$

Therefore, the equation of the line is:

f(x) = 3x - 8