Problems(1)
A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship's distance from Island X as it moves along its course?[asy]size(150);
pair X=origin, A=(-5,0), B=(5,0), C=(0,5);
draw(Arc(X, 5, 180, 360)^^B--C);
dot(X);
label("X", X, NE);
label("C", C, N);
label("B", B, E);
label("A", A, W);[/asy]<spanclass=′latex−bold′>(A)</span>
[asy]
defaultpen(fontsize(7));
size(80);
draw((0,16)--origin--(16,0), linewidth(0.9));
label("distance traveled", (8,0), S);
label(rotate(90)*"distance to X", (0,8), W);
draw(Arc((4,10), 4, 0, 180)^^(8,10)--(16,12));
[/asy]<spanclass=′latex−bold′>(B)</span>
[asy]
defaultpen(fontsize(7));
size(80);
draw((0,16)--origin--(16,0), linewidth(0.9));
label("distance traveled", (8,0), S);
label(rotate(90)*"distance to X", (0,8), W);
draw(Arc((12,10), 4, 180, 360)^^(0,10)--(8,10));
[/asy]<spanclass=′latex−bold′>(C)</span>
[asy]
defaultpen(fontsize(7));
size(80);
draw((0,16)--origin--(16,0), linewidth(0.9));
label("distance traveled", (8,0), S);
label(rotate(90)*"distance to X", (0,8), W);
draw((0,8)--(10,10)--(16,8));
[/asy]<spanclass=′latex−bold′>(D)</span>
[asy]
defaultpen(fontsize(7));
size(80);
draw((0,16)--origin--(16,0), linewidth(0.9));
label("distance traveled", (8,0), S);
label(rotate(90)*"distance to X", (0,8), W);
draw(Arc((12,10), 4, 0, 180)^^(0,10)--(8,10));
[/asy]<spanclass=′latex−bold′>(E)</span>
[asy]
defaultpen(fontsize(7));
size(80);
draw((0,16)--origin--(16,0), linewidth(0.9));
label("distance traveled", (8,0), S);
label(rotate(90)*"distance to X", (0,8), W);
draw((0,6)--(6,6)--(16,10));
[/asy] function