Precalculus H Test Chapter 1 NO CALCULATORS Show all work!
Name___________________________________________________
Part I
1) Graph the inverse.
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2)
x2  1
for x  1
f(x)=
for x< -1
 x3
a) graph
b) Is the function continuous?
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3) Graph
y
1
x 1
2
Part II
4) Write the domain.
h(x) =
1
2 16  x 2
5) Write all asymptotes and removable discontinuities.
y
 x  1 2 x  31  x  +2
 x  3 1  x 2 
Removable discontinuities
Vertical Asymptotes
Horizontal Asymptotes
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6) Write an equation for the following transformations on y = ex
Reflect over x-axis
Shrink vertically by a factor of 3
Shift right 3
7) Which of the ten basic functions:
yx
y  x2
y  ln x
y  sin x
y x
y  ex
y x
y  x3
y  cos x
1
y
x
a) Are one to one ?
b) Are increasing on the entire domain?
Part III Multiple Choice
8) Which of the following describes the relation
x 2 y 3  3x 2 y  1
a)
b)
c)
d)
odd
even
neither
both even and odd
9) Which of the following is the best algebraic model for the graph
below?
Precalculus H Chapter 1 Test
CALCULATORS ALLOWED
Name________________________________________________________
Show All Work
1) Fill in the blanks according to the graph.
lim f ( x) 
x
lim
f ( x) 

x  1
lim f ( x) 
x  
lim
f ( x) 

x  1
2)
f(x)=  x 4  x3  4 x 2  4 x  2
a) find the local maximum(s)
c)find the increasing interval(s)
b) find the local minimum(s)
d) find the decreasing interval(s)
3) Given f(x) = x  1
f(g(x)) = x 2  x  1
Find g(x)
4) Find a rule for the inverse. Include any restrictions on the domain.
f (x )  ln  x  2
5) For the parametric equations :
x  3t 1
y  5t 2
a) Find the endpoints
b) eliminate the parameter to
write the equation with y in terms of x
c) Sketch a graph
for 2  t  2
6)
g ( x) 
f(x) = x
a) find f(g(x))
1
x 1
b) find the domain of f(g(x))
7) A retention pond is fitted with a metal rectangular container of length 10
feet to help with drainage. The parabolic pond is 15 feet deep and 20 feet
across. What must the height of the rectangle be to fit flush with the top of
the pond and fit in the middle of the pond?
(10, 15)
(-10, 15)
-5
5