Download Homework Sheet Section 1

Homework Sheet Section 2.1
1. Write an algebraic equation and solve:
An HMO pamphlet contains the following recommended weight
for women: “Give yourself 100 pounds for the first 5 feet plus 5
pounds for every inch over 5 feet tall.” Using this description,
what height corresponds to a recommended weight of 135
pounds?
2. Perform the indicated operations and write the result in standard form:
6  12
48
3. Solve by the method of your choice:
1
1
1


x x2 3
4. Solve the polynomial equation by factoring and then using the zero-product
principle:
2 x  3  8x3  12 x 2 .
5. Solve the equation with rational exponents. Check all proposed solutions.
3
2
( x)  8
6. Solve the linear inequality. Use interval notation to express the solution set,
and graph each solution on the number line (other than  ).
4( x  1)  2  3x  6
7. Solve the absolute value inequality:
12  2 x 
6 3

7 7
8. Solve the polynomial inequality. Graph the solution set on a real number
line and express the solution in interval notation.
( x  7)( x  3)  0
9. Solve the rational inequality and graph the solution set on a real number
line. Also express the solution set in interval notation.
x
0
x 3
10.Determine whether the relation is a function. Give the domain and range.
{(3, -2), (5, -2), (7, 1), (4, 9)}
11.Determine whether the equation defines y as a function of x.
x 2  y  16
12.Evaluate the function at the give values of the independent variable and
simplify.
g ( x)  x 2  2 x  3
a) g(-1)
b) g(x+5)
c) g(-x)
13.Graph the given functions, f and g, in the same rectangular coordinate
system. Select integers for x, starting with –2 and ending with 2. Once you
have obtained your graphs, describe how the graph of g is related to the
graph of f.
f ( x)  x , g ( x)  x  2
14. Use the vertical line test to identify if the graph is one for which y is a
function of x.
y
x
15.
Use the graph of f to find the indicated function value. f(-2)
Answers:
1.
2.
5 ft 7 in
3.
{2  10}
4.
5.
6.
7.
8.
1
3
 
i
8 24
 1 1 3
 , , 
 2 2 2
{4}
[0,∞)
[
0
75   87 

 ,    ,  
14   14 

[-3,7]
-3
9.
7
(-∞,0] or (3,∞)
]
0
10.
11.
12.
function; {3,4,5,7}; {-2,1,9}
y is a function of x
a. 2
b. x2+12x+38
13.
14.
15.
not a function
-4
c. x2  2 x  3
(
3