20b. Mixed Exam-Style Questions On Graphs of Functions - Answers
20b. Mixed Exam-Style Questions On Graphs of Functions - Answers
20b. Mixed Exam-Style Questions On Graphs of Functions - Answers
1 a 4x2 − 9x + 5 = 3x − 4 2 a y
4x2 − 12x + 9 = 0 3
(2x − 3)2 = 0
x = 32
∴ x= 3
2
,y= 1
2
b y = 3x − 4 is a tangent to the curve
y = 4x2 − 9x + 5 at the point ( 32 , 12 )
−2 O 1 2 x
y
1
−3 −1 O 1 x
y
1
−2 −1 O 2 x
3 a x2 + 5x + 2 = 4x + 1 4 a y y = 1 + f(x)
x2 + x + 1 = 0
b2 − 4ac = 1 − 4 = −3
b2 − 4ac < 0 ∴ no real roots y = f(x + 3) 1
∴ does not intersect
b x2 + 5x + 2 = mx + 1 −3 O x
x2 + (5 − m)x + 1 = 0
only one root ∴ b2 − 4ac = 0 b 1+ x = x+3
(5 − m) − 4 = 0
2
(1 + 2
x) =x+3
5−m=±2 1+2 x +x=x+3
m = 3 or 7 x =1
x = 1 ∴ (1, 2)
Solomon Press
PMT
b 3 real roots
x3 − 3x2 − 2x + 5 = 0 ⇒ x3 − 3x2 = 2x − 5
the graphs of y = x3 − 3x2 and y = 2x − 5
intersect at three points
1 1
c x3 − = 2 ⇒ x3 − 2 =
x +1 x +1
1
the graphs y = x3 − 2 and y = intersect
x +1
at one point for x > 0 and at one point for x < 0
∴ one positive and one negative real root
Solomon Press