OCR Output Comparison | Datalab (Chandra & Surya)

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16. 已知函数 $y = -\frac{1}{2}x + 2$ , 当 $-1 \le x \le 1$ 时, $y$ 的取值范围是 ( )

A. $-\frac{5}{2} < y \le \frac{3}{2}$ B. $\frac{3}{2} < y < \frac{5}{2}$ C. $\frac{3}{2} \le y < \frac{5}{2}$ D. $\frac{3}{2} < y \le \frac{5}{2}$

17. 小明的父亲饭后散步, 从家中走 20 分钟到一个离家 900 米的报亭看 10 分钟的报纸后, 用 15 分钟返回家中, 下列图形中表示小明父亲离家的时间与距离之间的关系是 ( )

Four graphs (A, B, C, D) showing distance ( $y$ , up to 900) versus time ( $x$ , up to 45). The graphs illustrate the father's journey: walking 20 minutes to the stand (distance 900), staying 10 minutes (time 20 to 30), and walking back 15 minutes (time 30 to 45).

A: Distance increases linearly from (0, 0) to (20, 900), stays constant from (20, 900) to (30, 900), and decreases linearly from (30, 900) to (45, 0). This matches the description.

B: Distance increases linearly from (0, 0) to (20, 900), decreases linearly from (20, 900) to (45, 0). No stop.

C: Distance increases linearly from (0, 0) to (20, 900), stays constant from (20, 900) to (45, 900). No return trip.

D: Distance increases linearly from (0, 0) to (20, 900), stays constant from (20, 900) to (45, 900). No return trip.

18. 当 $a < 0, b > 0$ 时, 函数 $y=ax+b$ 与 $y=bx+a$ 在同一坐标系中的图象大致是 ( )

Four graphs (A, B, C, D) showing two intersecting lines. The conditions are $a < 0$ and $b > 0$ .

A: Line 1 ( $y=ax+b$ ) has a negative slope and positive y-intercept. Line 2 ( $y=bx+a$ ) has a positive slope and negative y-intercept. They intersect at $x=1$ in the first quadrant.

B: Line 1 has a negative slope and positive y-intercept. Line 2 has a positive slope and negative y-intercept. They intersect in the second quadrant.

C: Line 1 has a positive slope and negative y-intercept. Line 2 has a positive slope and positive y-intercept. They intersect in the first quadrant.

D: Line 1 has a negative slope and negative y-intercept. Line 2 has a negative slope and positive y-intercept. They intersect in the second quadrant.

三、解答题 (第 19 题 6 分, 其余每题 10 分, 共 56 分)

19. 地壳的厚度约为 8 到 40km, 在地表以下不太深的地方, 温度可按 $y=3.5x+t$ 计算, 其中 $x$ 是深度, $t$ 是地球表面温度, $y$ 是所达深度的温度.

(1) 在这个变化过程中, 自变量和因变量分别是什么?

(2) 如果地表温度为 $2^{\circ}\text{C}$ , 计算当 $x$ 为 5km 时地壳的温度.

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