ASSIGMENT #2
Name (please PRINT)
Marks: 100
Section.
Instructions: Show ALL your work. Answer the following questions:
1. (6p) For the following functions, find the average rate of change, a. r. c. =
f ( x + h) − f ( x)
h
, and
simplify. Leave the denominator in factored form.
a) f ( x ) =
x
x+3
b) f ( x) =
1
x2
2. (9p)a) Let f ( x ) = 4 2 x 4 + 5 . Is this function odd, even or neither? Justify your answer.
The function is………………….
b) Let g ( x ) =
x3 − x
.Is this function odd, even or neither? Justify youranswer.
x4 + 1
The function is………………….
c)
x2
Let h ( x ) = − 4
.Is this function odd, even or neither? Justify your answer.
x +1
The function is………………….
A2 pg1
3.(10p)Consider the piece-wise function whose equation is:
2 x

f ( x ) = 1
x2

−3≤ x < 0
x=0
x>0
a) Graph the function clearly showing the intercepts (if any).
b) Identify the domain, range.
Domain=……………………
Range=……………………….
4. (5p) Graph the function whose equation is: f ( x ) = 2 − x + 3 . Start with the basic function and
three points on each part and show and describe all the transformations you use to obtain the final
graph.
A2 pg2
5.(10p) A page with dimensions of 8.5 inches by 11 inches has a border of uniform width x surrounding
the printed matter of the page (text).
a) Express the area A of the printed part of the page as a function of the width x of the border.
b) Give the domain and range of A.
c) If the area of the printed page is 52.46 square inches, find the width of the border.
6.(10p) If y = −2 x 2 + 5 x + 3 , graph this function and give the coordinates of the vertex, equation of
axis of symmetry, find all intercepts, domain and range, and intervals where the function is increasing
and decreasing or neither.
Coordinates of the vertex: x =
y=
Axis of symmetry:
x intercepts: x= …………………..y=………
y intercept x= …………………..y=………
Domain=
Range=
The function is increasing for x in:
The function is decreasing for x in:
A2 pg3
7.(10p) Graph the following labelling any intercepts and/or asymptotes
a) y 2 = 2 x − 9
b)
c) 4 x 2 + 9 y 2 = 72
9 − x2 = 2 y
d) 9 y 2 − 4 x 2 = 36
8.(10p)Complete the square for each of the following, identify the conic. For circles, find the center and
radius. For ellipses find center and vertices. For hyperbolas, find center, vertices and the equations of
the asymptotes.
a) 16 x 2 + 4 y 2 + 48 x − 20 y + 57 = 0
Center at:Radius-= Asymptotes: -
-
A2 pg4
b) 9 x 2 − 4 y 2 − 18 x − 16 y − 43 = 0
Center at:
-
Radius-= -
-
Asymptotes: -
-
9. (10p)
2
a) Find the maximum value of f ( x) = −3x − 2 x + 5
b) Solve x 2 + 5 x − 6 ≥ 0
c) Factor completely: f ( x ) = 4 x 2 − 2 x − 3 Hint: f ( x) = a ( x − x1 )( x − x2 ) .
A2 pg5
2
10. (10p) A right triangle has one vertex on the graph of y = 9 − x , x > 0, at
the origin, and the third on positive x − axis at
( x, y ) , another at
( x, 0 ) . Express the area A of the triangle as a function
of x .
11. (10p) A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the
diagram, what is the height h of the arch 2 feet from the shore?
A2 pg6

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Section 2.6 Examples

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