Comparing Characteristics of Functions — Quiz

Question 63 • Mathematics II

Which function has the greatest maximum range value?

Answer

Image with description On a coordinate plane, the x-axis ranges from negative 6 to 10 by 2, and the y-axis ranges from negative 8 to 8 by 2. The graph has a parabola that opens down with a vertex (3 comma 1) and passes through (2 comma 0) and (4 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 10 to 6 by 2. A smooth curve that approaches the negative direction of the x-axis, passes through (0 comma negative 1), goes down, and passes through (2 comma negative 4).

Image with description On a coordinate plane, the x and y axes range from negative 8 to 8 in increments of 2. A smooth curve originates from (negative 3 comma 3), goes down, and passes through (2 comma 1) and (7 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 10 to 6 in increments of 2. The graph has an inverted v-shaped draw-up with a vertex at (negative 3 comma 1). One line passes through (negative 5 comma negative 1) and extends infinitely into the third quadrant. The other line passes through (0 comma negative 2) and extends infinitely into the fourth quadrant.

Explanation

The maximum range value is the greatest y-value the function reaches. In choice D, the curve begins at (−3, 3) and then goes downward, so its greatest y-value is 3. The other graphs have maximum y-values of at most 1, so D has the greatest maximum range value.

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