csat-suneung 2014 Q10

csat-suneung · South-Korea · csat__math-B 3 marks Curve Sketching Number of Solutions / Roots via Curve Analysis

As shown in the figure, the graphs of function $f ( x )$ defined on the closed interval $[ - 4,4 ]$ and function $g ( x ) = - \frac { 1 } { 2 } x + 1$ meet at three points, and the $x$-coordinates of these three points are $\alpha , \beta , 2$. The inequality $$\frac { g ( x ) } { f ( x ) } \leq 1$$ is satisfied. How many integers $x$ satisfy this inequality? (Here, $- 4 < \alpha < - 3,0 < \beta < 1$) [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

As shown in the figure, the graphs of function $f ( x )$ defined on the closed interval $[ - 4,4 ]$ and function $g ( x ) = - \frac { 1 } { 2 } x + 1$ meet at three points, and the $x$-coordinates of these three points are $\alpha , \beta , 2$. The inequality
$$\frac { g ( x ) } { f ( x ) } \leq 1$$
is satisfied. How many integers $x$ satisfy this inequality? (Here, $- 4 < \alpha < - 3,0 < \beta < 1$) [3 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30