Question

The graph of y=f(x) is shown above. Which of the following could be the graph of y=f′′(x)?.

Answer 1

The true statement about the graph of f(x) is $f(x) = \frac 35x + 3$

The graph of f(x) is a straight line that passes through the points (-5,0) and (0,3).

Start by calculating the slope (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

So, we have:

$m = \frac{3-0}{0--5}$

Simplify

$m = \frac{3}{5}$

The equation of the line is then calculated as:

$y = m(x -x_1) + y_1$

This gives

$y = \frac 35(x -0) + 3$

Open bracket

$y = \frac 35x + 3$

Express y as a function of x

$f(x) = \frac 35x + 3$

Hence, the true statement about the graph of f(x) is $f(x) = \frac 35x + 3$

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