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Question 10 • Mathematics III

Which function has exactly one x - and y -intercept?

Answer

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 6 by 2, and the y-axis ranges from negative 6 to 10 by 2. A smooth curve approaches the x-axis in the negative direction, passes through (0 comma 1), and has a vertical asymptote at x equals 2.

Image with description On a coordinate plane x lists from negative 6 to 10 by 2 and y axis lists from negative 8 to 8 by 2. The graph has two lines forming V shape and its vertex is at (2 comma negative 2). One line passes through (5 comma 0) and extends infinitely through the first quadrant. The other line passes through (0 comma 1) and extends infinitely through the second quadrant.

Image with description On a coordinate plane, the x-axis ranges from negative 10 to 6 by 2, and the y-axis ranges from negative 6 to 10 by 2. The graph has a smooth curve that starts from (0 comma 0 point 5), goes up, and passes through (1 comma 1).

Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 by 2. The graph has a parabola that opens up, with a vertex at (2 comma 0). It passes through (0 comma 4) and (4 comma 4).

Explanation

The parabola in choice B touches the x-axis only at its vertex, (2, 0), so it has exactly one x-intercept. It crosses the y-axis at (0, 4), giving it exactly one y-intercept as well. Choice A has two x-intercepts: one on each branch of the V.

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