college algebra test 3 questions with
accurate answers
Answer the following questions about the function below:
f(x)=x⁷+8x⁶+15x⁵
a) Use the leading coefficient test to determine the graphs end behavior.
b) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-
axis and turns around, at each intercept.
c)Find the y-intercept.
d) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
e) Graph the function. - answersa) Use the leading coefficient test to determine the
graphs end behavior.
-What is the graphs behavior to the left?
=falls to the left
-What is the graphs behavior to the right?
=rises to the right
b) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-
axis and turns around, at each intercept.
-What are the graph's x-intercepts?
=0,-5,-3
-What is the graph's behavior at the most negative x-intercept?
=the graph crosses the x-axis
-What is the graphs behavior at the next smallest x-intercept?
=the graph crosses the x-axis
-What is the graph's behavior at the other x-intercept?
=the graph crosses the x-axis.
c)Find the y-intercept.
-What is the graph's y-intercept?
=0
d) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
-What type of symmetry does the graph have?(to find y-axis symmetry, solve f(x)=f(-x).
To solve for origin symmetry, solve f(x)=-f(x).
=neither
e)Graph the function.
Write a formula that expresses the indicated variation:
T varies jointly as u and v. - answers-Use k as the constant of variation:
T=kuv
The volume of gas in a container at a constant temperature varies inversely as the
pressure. The volume is 20 cubic centimeters at a pressure of 7 pounds. Use a
, proportion to find the pressure when the volume is 44 cubic centimeters. -
answers20/x=44/7
20(7)=44x
140=44x
x=3.18
3.18 pounds
Explain why the given graph cannot be the graph of a polynomial function:
(see graph from problem 4) - answersThe function is not a polynomial function because
the graph is not continuous.
Divide using synthetic division:
(3x³+8x²-7x+7)/(x-2) - answers(2) 3 8 -7 7
↓ 6 28 42
__________________
3 14 21 49
quotient= 3x²+14x+21
remainder= 49
Find the oblique asymptote and sketch the graph of the following rational function.
g(x)=(x³-4)/(x²) - answerspg. 174 example 9
-y-intercepts
(set all x values to 0)
(0³-4)/(0²)=0
-x-intercepts
(set x³-4 equal to 0)
(x-1)(x-2)(x+2)
1,2,-2
.......
Find the domain of the rational function.
f(x)=(10-x)/(x+1) - answers*The domain of a rational function,
f(x)=numerator/denominator,consists of all real #s for which the denominator≠0.
-our denominator= x+1, the only number that could be substituted in for x that makes
the denominator =0 (undefined) is -1.
-therefore, 1 is the only number that we exclude from our domain.
-domain= (-∞,-1)∪(-1,∞)
Use the factor theorem and synthetic division to decide whether the second polynomial
is a factor of the first.
3x⁴+2x³-2x²+16x+8; x+2 - answers3x⁴+2x³-2x²+16x+8; x+2
accurate answers
Answer the following questions about the function below:
f(x)=x⁷+8x⁶+15x⁵
a) Use the leading coefficient test to determine the graphs end behavior.
b) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-
axis and turns around, at each intercept.
c)Find the y-intercept.
d) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
e) Graph the function. - answersa) Use the leading coefficient test to determine the
graphs end behavior.
-What is the graphs behavior to the left?
=falls to the left
-What is the graphs behavior to the right?
=rises to the right
b) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-
axis and turns around, at each intercept.
-What are the graph's x-intercepts?
=0,-5,-3
-What is the graph's behavior at the most negative x-intercept?
=the graph crosses the x-axis
-What is the graphs behavior at the next smallest x-intercept?
=the graph crosses the x-axis
-What is the graph's behavior at the other x-intercept?
=the graph crosses the x-axis.
c)Find the y-intercept.
-What is the graph's y-intercept?
=0
d) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
-What type of symmetry does the graph have?(to find y-axis symmetry, solve f(x)=f(-x).
To solve for origin symmetry, solve f(x)=-f(x).
=neither
e)Graph the function.
Write a formula that expresses the indicated variation:
T varies jointly as u and v. - answers-Use k as the constant of variation:
T=kuv
The volume of gas in a container at a constant temperature varies inversely as the
pressure. The volume is 20 cubic centimeters at a pressure of 7 pounds. Use a
, proportion to find the pressure when the volume is 44 cubic centimeters. -
answers20/x=44/7
20(7)=44x
140=44x
x=3.18
3.18 pounds
Explain why the given graph cannot be the graph of a polynomial function:
(see graph from problem 4) - answersThe function is not a polynomial function because
the graph is not continuous.
Divide using synthetic division:
(3x³+8x²-7x+7)/(x-2) - answers(2) 3 8 -7 7
↓ 6 28 42
__________________
3 14 21 49
quotient= 3x²+14x+21
remainder= 49
Find the oblique asymptote and sketch the graph of the following rational function.
g(x)=(x³-4)/(x²) - answerspg. 174 example 9
-y-intercepts
(set all x values to 0)
(0³-4)/(0²)=0
-x-intercepts
(set x³-4 equal to 0)
(x-1)(x-2)(x+2)
1,2,-2
.......
Find the domain of the rational function.
f(x)=(10-x)/(x+1) - answers*The domain of a rational function,
f(x)=numerator/denominator,consists of all real #s for which the denominator≠0.
-our denominator= x+1, the only number that could be substituted in for x that makes
the denominator =0 (undefined) is -1.
-therefore, 1 is the only number that we exclude from our domain.
-domain= (-∞,-1)∪(-1,∞)
Use the factor theorem and synthetic division to decide whether the second polynomial
is a factor of the first.
3x⁴+2x³-2x²+16x+8; x+2 - answers3x⁴+2x³-2x²+16x+8; x+2
