WeBWorK Standalone Renderer

The figure shows an interactive graph of $y = f(t)$ . (It may take a minute to load -- be patient.) You can change the value of $x$ in the graph by clicking and dragging the red dot along the horizontal $t$ -axis. Assume that the lines in each piece of $f$ continue beyond the graphing window. Define a function that accumulates signed area between the $t$ -axis and the graph of $y = f(t)$ by

$\displaystyle F(x) = \int_0^x f(t) \, dt$

(a) For what values of $x$ does $F(x) = 0$ ?
$x \approx$

(b) For what values of $x$ is $F(x) \geq 0$ ?
All $x$ in the interval

(c) For what values of $x$ does $F(x) = 6$ ?
$x \approx$

(d) Why is $F(x)$ positive when $x$ is negative?
A. Because accumulation functions like $F(x)$ are always positive
B. Because integrals are always positive
C. Because integrating right-to-left is negative
D. Because $f(x)$ is negative and integrating right-to-left is negative
E. None of the above

Graph of $y = f(t)$

You can earn partial credit on this problem.