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MATH 1113 PreCalculus
Test 2 Version A Fall 2006
Read the following
Show all work clearly in the space provided. No credit will be given to problems with no work, excluding the Fill in the
Blank and True/False questions. Use only fractions. NO CREDIT WILL BE GIVEN FOR ANY WORK DONE IN
DECIMALS. Any work done on scratch paper that you want me to look at needs a note on the test saying so.
1. Given the function 2 2 3
2 y = โ x + x + , find the following:
a. Find the x -intercepts showing all work. (6 pts) d. Graph, labeling ALL the intercepts and the vertex. (5 pts) y
b. Find the vertex showing all work. (6 pts)
e. The axis of symmetry is _____________ (2 pts)
c. Find the y -intercept (2 pts) f. Domain ______________________(2 pts)
Range _______________________ (2 pts)
2. Given the function
2 2 2 y = โ 4 x ( x โ 2 ) ( x + 2 ) , find the following:
a. x -intercepts and determine if the graph crosses or touches
at each. (6 pts)
d. Graph, labeling ALL the intercepts and asymptotes, if any. (5 pts) y
b. Power Function (3 pts)
The graph resembles the graph of ___________
for large values of | x |.
x
c. Find the y -intercept (2 pts) e. Domain ______________________ (2 pts)
Range _______________________ (2 pts)
Note: This test is given just as a sample test 2. It is NOT intended to be a study guide. Some material on this test we may not have covered in our class, and there IS additional material that we DID cover which was not tested on this test.
3. True/False (2 pts each)
a) __________ The graph of ( ) 2 3 4
2 f x = x โ x โ has a maximum value.
b) __________ The vertex of ( ) 4 ( 150 ) 257
2 f x = x โ โ is (-150, -257).
c) __________ The x -intercepts of the graph of a function y = f ( x ) are the real solutions of the equation f ( x ) = 0.
d) __________ The x -intercepts of the graph of a polynomial function are called turning points.
e) __________
2
2 x G x
= is a polynomial function.
4. Fill in the Blank (1 pt each blank)
a) The graph of the power function
n f ( x )= ax with n odd, always contains the points ________, ________, _________.
b) To graph ( ) ( 2 ) 4
4 f x = โ x โ + by transformations, you would first start with the power function ________.
Next, you would reflect the graph about the _____axis. Finally, you would move the graph ______ horizontal units to the
_______ and _______ vertical units ______.
c) The line _________ is a horizontal asymptote of
1
3
2
x
x T x and this graph has a vertical asymptote at _________.
d) Fill in the blank with the correct notation: If f ( x ) = x + 1 and
3 g ( x )= x , then ______________ =
3 ( x + 1 )
- Derive the quadratic formula, or in other words, find the x -intercepts of f x = ax + bx + c
2 ( ). Show all work clearly
and with proper mathematical notation. (6 pts)
(start here) (continue over here)
8. Given the function
4 3
2 โ +
x x
x x f x , find the following:
a. x -intercept(s) (2 pts) d. Graph accurately, labeling all asymptotes, points where the graph crosses the HA (if any), all intercepts, and the additional points below. (5 pts) (2, 8), (1.5, 11.7), (2.5, 9)
y
b. Horizontal asymptote(s) ________ (4 pts)
Vertical asymptote(s)
_________________________ (4 pts)
Find out if the graph crosses its HA. Show
work below. (4 pts)
x
c. Find the y -intercept (2 pts)
e. Domain ______________________ (2 pt)
9) If gx mx x
ax f x =
( ) , find f o g. (6 pts)
