csat-suneung 2012 Q12

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

The graphs of the quadratic function $y = f ( x )$ and the cubic function $y = g ( x )$ are shown in the figure.
$f ( - 1 ) = f ( 3 ) = 0$, and the function $g ( x )$ has a local minimum value of $- 2$ at $x = 3$. What is the number of distinct real roots of the equation $\frac { g ( x ) + 2 } { f ( x ) } - \frac { 2 } { g ( x ) } = 1$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

The graphs of the quadratic function $y = f ( x )$ and the cubic function $y = g ( x )$ are shown in the figure.

$f ( - 1 ) = f ( 3 ) = 0$, and the function $g ( x )$ has a local minimum value of $- 2$ at $x = 3$. What is the number of distinct real roots of the equation $\frac { g ( x ) + 2 } { f ( x ) } - \frac { 2 } { g ( x ) } = 1$? [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