Math 1314
Review Test 2
1. For the given quadratic function, find the vertex. Sketch the graph. Give the equation of the
parabola’s axis of symmetry. Find the x-intercept(s) and range of the function. f ( x)  ( x  4) 2  3
2. Find the intercepts and vertex of f ( x)  9 x 2  18 x  7 .
Solve and graph solution on a number line. Write answer in interval notation.
1. 9 x 2  3x  2
2. 4 x 2  x  0
3. Find the domain of the function.
1
a) f ( x)  2
4x  7x  3
b) h( x)  7 x  4 (Write answer in interval notation)
c) f ( x) 
2 x  13
(Write answer in interval notation)
x 1
GRAPH the following functions.
4. y  x  3  5
5. y  2 x  2  1
d) h( x)  3 x  18  4 x  8
6. y   3 x  4  5
1
7. y   ( x  2)3  4
2
8. f ( x )  3  x  1  4
2
 3 x  2 x  2
9. f ( x )  
 x  1  1 x  2
10. Refer to the function f. Use the graph of f to graph the following function: y  2 f ( x  3)  1
11. Find the x-intercepts: (a) f ( x)  20 x 3  32 x 2  45 x  72
(b) f ( x)  2 x 3  3 x 2  10 x  15
(c) f ( x)  3 x 4  5 x 2  2
12. Given: f ( x)  ( x  1)( x  1)3 ( x  4) 2 ( x  2)
(d) Graph the function as shown in class.
(a) What is the leading term?_______________
Describe the end behavior.
(b) Find the x-intercepts: and state their
multiplicity.
(c) Find the y-intercept:____________________
13. Use synthetic division to find the quotient and remainder.
2x 4  3 x 3  4 x 2  1
x 1
14. Use the remainder theorem to find
f (1) given that f ( x)  11x 5  x 4  3 x 2  4 x  10
15. Factor f ( x)  8 x 4  38 x 3  15 x 2  72 x  27 completely, given that 3 is a zero of f ( x ) of
multiplicity of two.
Math 1314
Review Test 2
1. For the given quadratic function, find the vertex. Sketch the graph. Give the equation of the
parabola’s axis of symmetry. Find the x-intercept(s) and range of the function. f ( x)
( x 4) 2 3
2. Find the intercepts and vertex of f ( x) 9 x 2 18 x 7 .
Solve and graph solution on a number line. Write answer in interval notation.
1. 9 x 2 3 x 2
2.
4 x2
x 0
3. Find the domain of the function.
1
a) f ( x )
2
4x 7x 3
b) h( x)
c) f ( x)
7 x 4 (Write answer in interval notation)
2 x 13
(Write answer in interval notation)
x 1
GRAPH the following functions.
4. y x 3 5
5. y
d) h( x)
2 x 2 1
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3 x 18
6. y
3
4x 8
x 4 5
7. y
1
( x 2)3 4
2
3
8. f ( x ) 3 x 1
2
4
9. f ( x )
x
(b) f ( x )
2 x 3 3 x 2 10 x 15
20 x3 32 x 2 45 x 72
(c) f ( x ) 3 x 4 5 x 2 2
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2
x
x 1 1
10. Refer to the function f. Use the graph of f to graph the following function: y
11. Find the x-intercepts: (a) f ( x )
2
x
2
2 f ( x 3) 1
12. Given: f ( x )
( x 1)( x 1)3 ( x 4) 2 ( x 2)
(d) Graph the function as shown in class.
(a) What is the leading term?_______________
Describe the end behavior.
(b) Find the x-intercepts: and state their
multiplicity.
(c) Find the y-intercept:____________________
13. Use synthetic division to find the quotient and remainder.
2x 4 3x 3 4 x 2 1
x 1
14. Use the remainder theorem to find
f ( 1) given that f ( x) 11x5
x 4 3 x 2 4 x 10
15. Factor f ( x ) 8 x 4 38 x 3 15 x 2 72 x 27 completely, given that 3 is a zero of f ( x ) of
multiplicity of two.
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