Test: Functions II - Ambitious

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Question 1:   Find the period of the function f( x )=cos( θ 3 )
6π
3π
2π
1 3 π
Question 2:   Find the period of the function f( x )=6cot( 3θ+4 )
π 3
7π
π
4 3 π
Question 3:   Find the period of the function f( x )=2cos( θ 2 )+5cos( θ 3 )
4π
6π
12π
18π
Question 4:   Find the period of the function f( x )= 1 5 sin( 3θ )+ 1 4 sin( θ 5 )
5π
30π
2 3 π
10π
Question 5:   Find the amplitude of the function f( x )=3sin( θ 15 )
3
1
30
6
Question 6:   Find the amplitude of the function f( x )=x+1 for 0x<2 and f( x+n )=f( x ) for any integer.
1
0
2
3
Question 7:   Find the inverse of the function f( x )=2 e x .
f 1 ( x )= 1 2 lnx
f 1 ( x )= 1 2 e x
f 1 ( x )=2lnx
f 1 ( x )= e 1 2 x
Question 8:   If the function is defined as f( x )= x 2 +ax+b , find the coefficients a and b if f( 2 )=3 and f( 3 )=7
{ a=1 b=1
{ a=1 b=1
{ a=0 b= 1 2
{ a=1 b=2
Question 9:   On the diagram below is a sketch of a function f( x ) . Sketch a graph of y=| f( x ) |




Question 10:   On the diagram below is a sketch of a function f( x ) . Sketch graph of y=f( x )