ACCEL PRE-CALCULUS/TRIG 3 Name:_________________________________ Date:_____________
Review: Sections 1.6, 1.7, 1.9 & 2.1-2.5
1) 2)
parent: parent:
x y x y
Vertex: (_________) Vertices: (_________), (__________) Quads: _______
2) 4)
parent parent:
x y x y
Vertex: (_________) Vertex: (_________)
5) 6) Write the equation of the function below.
parent:
x y
Vertex: (_________) f(x)=_______________________
Describe (in words) the transformations that have taken place.
7. ___________________________________________________________________
8. ____________________________________________________________________
9. ____________________________________________________________________
10. ____________________________________________________________________
x
11. Are the functions f ( x) 4( x 2) and g ( x) 2 inverses of each other? Prove or
4
disprove formally. (Hint Do and )
Find the inverse. Then determine if the inverse is a function.
12) f ( x) 3 x 7 13) f(x)= 14) f ( x) x 2 4
Given f(x)=7x+1 and g(x)=x3 Is the inverse of the function a function?
How did you know?
15) g-1 f-1= 16) a) b)
GRAPH THE FOLLOWING. x y
17) y =2(x + 1)2 - 4
Vertex:_________
Axis of Symmetry: ___________
zeros: _______________
18) y = x2 – 6x + 7
x y
Standard form: f(x)=___________________________
Vertex:_________
Axis of Symmetry: ___________ zeros: _______________
19) y = 3x2 + 24x + 49
x y
Standard form: f(x)=___________________________
Vertex:_________
Axis of Symmetry: ___________ zeros: _______________
20) Write an equation in standard form that has a __________________________________
vertex (3, -6) and goes through the point (1, -2).
21)DRAW THE END BEHAVIOR OF THE GRAPH..
When n is odd, When n is even,
1) If the leading coefficient is positive 1) If the leading coefficient is positive
f(x) ____ as x - f(x) ____ as x -
f(x) ____ as x f(x) ____ as x
2) If the leading coefficient is negative 2) If the leading coefficient is negative
f(x) ____ as x - f(x) ____ as x -
f(x) ____ as x f(x) ____ as x
GRAPH THE FOLLOWING POLYNOMIALS BY HAND. USE THE LEADING COEFFICIENT
TEST, ZEROS, Y-INT, AND TEST POINTS!
22) f(x) = - x4 + 9x2
23) f(x) = 2x3 – 2x2 - x
WRITE AN EQUATION WITH THE GIVEN ROOTS.
24) x= 7, -4 f(x)=__________________ 25) x= –9i, 9i f(x)=__________________
COMPLETE THE FOLLOWING. SHOW ALL WORK!
26) Use the Remainder Theorem to determine if (x – 3) 26. YES or NO
is a factor of (2x4 + 9x3 – 9x2 – 46x + 24)?
27) Is –2 a root of x4 + 5x2 – 36? 27. YES or NO
28) Divide (x4 + x3 – 2x2 + 4x – 24) by (x – 2) 28. ____________________
and name the remaining polynomial
SIMPLIFY THE FOLLOWING. WRITE THE ANSWER IN STANDARD FORM.
29) i37 30) i48 31) What is the conjugate of -6 + 2i
3 2i
32) 5i i 2 33) i(6 i)(3 2i) 34)
5i
35) 36)
FIND THE ROOTS AND THE Y-INT, THEN SKETCH THE GRAPH.
37) y = x3 – 6x2 + 11x – 6
38) y = x3 + 3x2 + 5x + 3
39) y = 4x4 – 12x3 + 3x2 + 13x – 6
40) The path of a football is represented by the equation y = -(x – 2)2 + 10 where x represents time in seconds and y represents
the position in feet.
a) After how many seconds has the football reached its maximum height?
b) What is the maximum height?
c) At what position does the object begin its path?
d) What are the x-intercepts?
e) If the maximum position was 4 feet higher, what would the equation be?