Practice Exam

Question 12 • Algebraic Reasoning

The area of a trapezoid can be found using the formula cap A times x is equal to 1 half cap b x h x , where cap b times x is the sum of the bases and h of x is the height. Which graph could include the functions?

Answer

Image with description On a first-quadrant coordinate plane, the x and y axes range from 0 to 40 in increments of 10. The graph has 3 straight lines (A of x), (B of x), and (h of x) with positive slopes originating from the origin. The straight line (h of x) is close to the x-axis and passes close to (40 comma 11). The straight line (B of x) is in the middle and passes close to (20 comma 15). The straight line (A of x) is close to the y-axis and passes close to (10 comma 10).

Image with description On a first-quadrant coordinate plane, the x and y axes range from 0 to 20 in increments of 5. The graph has a curve (A of x), and 2 straight lines (B of x), and (h of x), with positive slopes originating from the origin. The straight line (h of x) is close to the x-axis and passes through (20 comma 5). The straight line (B of x) is in the middle and passes through (20 comma 15). The curve (A of x) passes through (5 comma 15) and then rises.

Image with description On a first-quadrant coordinate plane, the x and y axes range from 0 to 20 in increments of 5. The graph has a curve (A of x), and 2 straight lines (B of x), and (h of x,) with positive slopes originating from the origin. The straight line (h of x) is close to the x-axis and passes through (20 comma 5). The straight line (B of x) is in the middle and passes close to (20 comma 15). The curve (A of x) passes close to (14 comma 20).

Image with description On a first-quadrant coordinate plane, the x and y axes range from 0 to 40 in increments of 10. The graph has 3 straight lines (A of x), (B of x), and (h of x) with positive slopes originating from the origin. The straight line (h of x) is close to the x-axis and passes through (20 comma 5) and (40 comma 10). The straight line (B of x) is in the middle and passes through (40 comma 30). The straight line (A of x) is close to the y-axis and passes close to (5 comma 40).

Explanation

Since B(x) and h(x) are straight lines through the origin, the graph of A(x) = ½B(x)h(x) should be curved. In choice C, B(20) is about 15 and h(20) is about 5, so their values at x = 14 are about 10.5 and 3.5. This gives A(14) ≈ ½(10.5)(3.5) = 18.375, close to the graph’s stated value of 20. The other choices either show A as a straight line or put it far from the value predicted by the formula.

AI-written and checked against the verified answer.

More from this Course

Practice Exam

Exam

Exam