Math 3201
Test, Chapter 5
Name:_____________________
Part I: Place the letter of the correct answer in the space provided on page 4. (15 mks)
1. What is the leading coefficient of the polynomial:
A) -7
B) -5
?
C) 3
D) 4
2. What is the end behavior of the graph of:
A) Q2 to Q1
B) Q3 to Q1
?
C) Q2 to Q4
3. What is the y-intercept of
A) -1
D) Q3 to Q4
?
B) 0
C) 1
D) 2
4. How many possible x-intercepts can
A) 0
have?
B) 0, 1, or 2
C) 0, 1, 2, or 3
D) 1, 2, or 3
5. Determine the leading coefficient of this polynomial function:
f(x) = 4x – 23 + x
A) 4
B) –2
C) 1
D) 5
6. From which quadrants does the graph of
A) II to I
B) III to I
extend?
C) II to IV
D) III to IV
7. How many turning points can a cubic polynomial have?
A) 0, 1, or 2
B) 1, 2, or 3
C) 0 or 2
1
D) 2
8. What is the range of the function y  f ( x ) shown in the graph below?
y
 y y  2, y  R
(A)
10
y=f(x)
9
8
7
 y y  2, y  R
(B)
6
5
4
(C)
 y y  2, y  R
(D)
 y y  2, y  R
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-2
9. Determine the equation of this polynomial function:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
A) f(x) = –x2 – 3x – 1
B) g(x) = x2 – 2x + 1
C) h(x) = –x3 – 2x2 + 1
D) j(x) = x3 + 2x
10. What is the maximum number of x-intercepts that a polynomial
function of degree 2 will have?
A) 0
B) 1
C) 2
D) 3
11. What is the degree of the polynomial
A) 0
B) 1
-1
?
C) 2
D) 4
2
1
2
3
4
x
12. What is the domain of
?
A)
B)
C)
D)
13. Which function passes through the point 1, 7  ?
(A)
f ( x)   x 3  3 x 2  x  4
(B)
f ( x)   x 3  2 x 2  x  7
(C)
f ( x)  x 3  2 x 2  4
(D)
f ( x)  x 3  3 x 2  7
14. Which graph best represents a function with the characteristics listed below?
(A)

Three x-intercepts

Extending from Quadrant II to Quadrant IV
y
(B)
y
x
(C)
y
x
(D)
x
y
x
3
15. Given the table, the scatter plot and the curve of best fit of the polynomial f(x),
what is the value of f(5)?
y
X
(A)
Y
2
5
4
24
6
12
8
0
10
23
2
(B)
y=f(x)
30
25
20
15
10
5
2
9
(C)
4
6
18
8
10
(D)
12
x
20
Selected Response Answer Sheet
1. ____B
6. ____D
11. ____B
2. ____A
7. ____C
12. ____A
3. ____C
8. ____D
13. ____A
4. ____D
9. ____C
14. ____A
5. ____D
10. ____C
15. ____D
Part II: Complete each question in the space provided. (28 mks)
1. Determine the following characteristics of each function:
(12 mks)
a)
b)
number of possible x-intercepts: 1, 2, OR 3
number of possible x-intercepts: 0 or 1
y-intercept: 1 OR (0,1)
y-intercept: -2 OR (0,-2)
domain:  x | x 
domain:  x | x 
range:  y | y 


range:  y | y 


number of possible turning points: 0 or 2
number of possible turning points: 0
end behaviour: Q2 to Q4, rises left, falls right
end behaviour: Q3 to Q1, rises right, falls left
4
1
2
3
4
5
2.5432154321––Determine
the following characteristics for the54321– 54321polynomial functions graphed. (12 mks)
1
2
3
4
5
1– 5
2
3
4
5
1
2
3
4
a)
b)
y
y
5
5
4
3
2
1
– 5 – 4 – 3 – 2 –– 11
– 2
– 3
– 4
– 5
4
3
2
1
1
2
3
4
– 5– 4– 3– 2– 1
– 1
5 x
1
2
3
4
5 x
– 2
– 3
– 4
f '(x)
– 5
Degree: 3
Degree: 2
Sign of leading coefficient: negative
Sign of leading coefficient: positive
Constant term of function: 0
Constant term of function: -1
End behaviour: Q2 to Q4, rises left, falls right
End behaviour: Q2 to Q1, rises right, rises left
Domain:  x | x 
Domain:  x | x 
Range:  y | y 



Range:  y | y  1
3. Sketch two possible graphs that are different, yet are both cubic functions with
negative leading coefficients and the same negative y-intercepts. Explain why the graphs you
have sketched are different.
(4 mks)
Graph 1:
Graph 2:
Each graph has a different number of x-intercepts and a different number of turning points.
5