Which of the following graphs represents the function f(x) = x4 - 2x3 - 3x2 + 4x + 1?
Answers
Answer: Graph D will be correct graph for the given function.
Explanation:
Given function [tex]f(x) = x^4-2x^3-3x^2+4x+1[/tex]
Since it is a bi-quadratic equation thus it must have 4 roots and (0,1) is one of its point.
Moreover, the degree of the function is even thus the end behavior of the function is[tex]f(x)\to+\infty[/tex], as [tex]x\to-\infty[/tex] and [tex]f(x)\to+\infty[/tex] as [tex]x\to+\infty[/tex]
In graph A, function has four root but it does not have the end behavior same as function f(x).( because in this graph [tex]f(x)\to-\infty[/tex], as [tex]x\to-\infty[/tex] and [tex]f(x)\to-\infty[/tex], as [tex]x\to+\infty[/tex].) so, it can not be the graph of given function.
In graph B, neither it has four root nor it has the end behavior same as function f(x).(because in this graph [tex]f(x)\to+\infty[/tex] as [tex]x\to-\infty[/tex] and [tex]f(x)\to-\infty[/tex] as [tex]x\to+\infty[/tex].) so, it can not be the graph of given function.
In graph C, neither it has four root nor it has the same end behavior as function f(x).(because in this graph [tex]f(x)\to-\infty[/tex] as [tex]x\to-\infty[/tex] and [tex]f(x)\to+\infty[/tex] as[tex]x\to\infty[/tex].) so, it also can not be the graph of given function.
In graph D it has four root as well as it has the same end behavior as the given function. Also it passes through the point (0,1).
Thus, graph D is the graph of given function.
Related Questions
Select Is a Function or Is not a Function to correctly classify each relation.
Title
Is a Function
Is not a Function
{(3, 7),(3, 6),(5, 4),(4, 7)}
{(1, 5),(3, 5),(4, 6),(6, 4)}
{(2, 3),(4, 2),(4, 6),(5, 8
{(0, 4),(3, 2),(4, 2),(6, 5)}
Answers
Answer:
{(3, 7),(3, 6),(5, 4),(4, 7)} → is not a Function{(1, 5),(3, 5),(4, 6),(6, 4)} → is a Function{(2, 3),(4, 2),(4, 6),(5, 8)} → is not a Function{(0, 4),(3, 2),(4, 2),(6, 5)} → is a FunctionStep-by-step explanation:
A relation from a set X to a set Y is called a function, if each element of X is related to one and exactly one element in Y. Though many elements of X can be related to one element in Y (many to one).
{(3, 7),(3, 6),(5, 4),(4, 7)} → is not a Function (as (3, 7), (3, 6) share same x)
{(1, 5),(3, 5),(4, 6),(6, 4)} → is a Function
{(2, 3),(4, 2),(4, 6),(5, 8)} → is not a Function (as (4, 2), (4, 6) share same x)
{(0, 4),(3, 2),(4, 2),(6, 5)} → is a Function
Answer: ^^^ that person was correct
Step-by-step explanation:
Select the graph of the solution. Click until the correct graph appears.
x ≥ 4
Answers
Answer:
The answer is the option B
see the attached figure
Step-by-step explanation:
we have
[tex]x\geq4[/tex]
The solution is the interval ------> [4,∞)
All real numbers greater than or equal to [tex]4[/tex]
therefore
the answer in the attached figure
What is the end behavior of f(x) = (x − 3)2(x + 5)(x − 2)3?
Answers
I hope this helps.
T he end behavior of f(x) can be described as:
As x → -∞, f(x) → +∞
As x → +∞, f(x) → +∞
To determine the end behavior of f(x) = (x − 3)²(x + 5)(x − 2)³, we need to consider the degree and leading coefficient of the polynomial.
1. Degree of the Polynomial:
The degree is the highest sum of exponents of the variable x in any term. In this case:
(x - 3)² contributes a degree of 2 (x² term)
(x + 5) contributes a degree of 1 (x term)
(x - 2)³ contributes a degree of 3 (x³ term)
Adding these degrees, we get a total degree of 2 + 1 + 3 = 6.
2. Leading Coefficient:
The leading coefficient is the coefficient of the term with the highest degree. Since all factors have a leading coefficient of 1, the leading coefficient of the entire polynomial will also be 1 (positive).
3. End Behavior Based on Degree and Leading Coefficient:
Even Degree & Positive Leading Coefficient: When the degree is even and the leading coefficient is positive, both ends of the polynomial will approach positive infinity. In other words, as x approaches both positive and negative infinity, f(x) will also approach positive infinity.
Therefore, the end behavior of f(x) can be described as:
As x → -∞, f(x) → +∞
As x → +∞, f(x) → +∞
Complete question:
What is the end behavior of [tex]f(x) = (x - 3)^{2} (x + 5)(x - 2)^{3}[/tex]?
Emily has a coupon for 20% off her purchase. She finds a backpack on the discount rack. It's original price is $60 but is 30% off. Emily thinks 30% & 20 % make 50% so the backpack will be $30. Is Emily correct? Explain your answer.
Answers
lim cos(pi+h)+1 / h
h->0
evaluate the limit
Answers
Lim cos(pi+h)+1 / h = Lim (cos(pi+h)+1)' / h' = Lim -sin(pi+h)+1 / 1= -1/1=-1
h->0 h->0 h->0
The graph of the function f(x) = (x – 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < –1 and where x > 4. The function is decreasing for all real values of x where –1 < x < 4. The function is decreasing for all real values of x where x < 1.5.
Answers
we have
[tex]f(x)=(x-4)(x+1)[/tex]
using a graph tool
see the attached figure
we know that
The function is increasing for all real values of x where [tex]x > 1.5[/tex]
and
The function is decreasing for all real values of x where [tex]x < 1.5[/tex]
therefore
Statements
case a) The function is increasing for all real values of x where x < 0
The statement is false
case b) The function is increasing for all real values of x where x < –1 and where x > 4
The statement is false
case c) The function is decreasing for all real values of x where –1 < x < 4
The statement is false
case d) The function is decreasing for all real values of x where x < 1.5
The statement is true
Answer:
The correct option is:
The function is decreasing for all real values of x where x < 1.5.
Step-by-step explanation:
We are given a function f(x) which is a product of two linear polynomial as:
[tex]f(x)=(x-4)(x+1)[/tex]
Now, we know that on multiplying the two linear polynomial we will obtain a quadratic polynomial.
So, the function f(x) will be represented as:
[tex]f(x)=x(x+1)-4(x+1)\\\\f(x)=x^2+x-4x-4\\\\f(x)=x^2-3x-4[/tex]
So, we will plot the graph of the function and check which statements about the function hold true.
1)
The function is increasing for all real values of x where x < 0.
This statement is false.
Since we get from the graph that function f(x) is decreasing for x<0.
2)
The function is increasing for all real values of x where x < –1 and where x > 4.
This option is incorrect as the function is decreasing for x<-1
whereas it is increasing for x>4.
3)
The function is decreasing for all real values of x where –1 < x < 4.
This option is incorrect.
Since, the function is both decreasing as well as increasing in the interval (-1,4).
4)
The function is decreasing for all real values of x where x < 1.5.
This option is correct.
Since it could be observed from the graph that the function is decreasing for x<1.5.
Find the lim [(ln(x+5) - ln5) / x ] as x approaches 0
...?
Answers
[tex] \lim_{x \to 0}\frac{\ln(x+5) - \ln5}{x} \\ \\ \lim_{x \to 0}\frac{ \ln{ \frac{x+5}{5} }}{x} \\ \\ \lim_{x \to 0}\frac{ \ln{( 1+\frac{x}{5} )}}{x} \\ \\ \lim_{x \to 0}\frac{ \ln{( 1+\frac{x}{5} )}}{\frac{x}{5}\times 5} \\ \\ \frac{1}{5} \lim_{x \to 0}\frac{ \ln{( 1+\frac{x}{5} )}}{\frac{x}{5}} \\ \\ \frac{1}{5} \times 1 \\ \\\frac{1}{5}[/tex]
To find the limit of the given expression [(ln(x+5) - ln5) / x ] as x approaches 0, we can apply L'Hospital's Rule.
Explanation:To find the limit of the given expression, we can use L'Hospital's Rule. Let's first rewrite the expression:
[ln(x+5) - ln(5)] / x
As x approaches 0, when plugging in 0, we get an indeterminate form of 0/0. So, we can apply L'Hospital's Rule:
lim [(ln(x+5) - ln5) / x ] as x approaches 0 = lim [(1/(x+5)) / 1]
= lim (1 / (x+5)) as x approaches 0
Since x approaches 0, the expression approaches 1 / (0+5) = 1/5.
What is 8.24 written as a percent?
Answers
What is the circumference of the circle in terms of pi? The radius is 2.2
choices are 1.1, 1.21, 2.2 and 4.4
im so confused so could someone please explain what i did wrong?
Answers
circumference=pi.r^2
circumference=pi. (2,2)^2
circumference=4,84.pi
lets name it as O
O = 2*r * pi
when we express r in this formula we get:
O = 2*2.2*pi
O = 4.4*pi
From this we can see that for given radius, answer is 4.4. The formula only depends on pi and that is what "in terms of pi" means.
A triangle with a base of 9 units and a height of 22 units ?
Answers
81+484=x^2
565=x^2
x is approximately 24 units
If f'(x)=g'(x) for all x in an interval I, what is the relationship between f and g ...?
Answers
The amount of time Ricardo spends brushing his teeth follows a Normal Distribution with unknown mean and standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and standard deviation of this distribution.
Answers
If 12 is added to the square of a positive integer, the result is 133. Find the positive integer.
Answers
Check: 192 + 4(19) = 437 361 + 76 = 437 437 = 437This answer checks
The value of the positive integer is,
⇒ 11
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Here, 12 is added to the square of a positive integer, the result is 133.
Let a positive integer = x
Hence, We can formulate;
⇒ 12 + x² = 133
⇒ x² = 133 - 12
⇒ x² = 121
⇒ x = √121
⇒ x = 11
Thus, The value of the positive integer is,
⇒ 11
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Write9^3 *p without exponents
Answers
What is the slope of the line? y = 3x + 9
A. 9
B. 3
C. 12
D. 6
Answers
m=slope
y=3x+9
slope=3
answer is 3, B
How many meters are equivalent to 375 centimeters
Answers
Then, 375 cm = 375/100 m = 3.75 m
So, your final answer is 3.75 m
Hope this helps!
The total distance an object travels varies directly with the length of time it travels. If an object travels 32 meters in 18 seconds, how long will it take to travel 80 meters? A. 40 seconds B. 42 seconds C. 45 seconds D. 48 seconds
Answers
Note that the unit "meter" cancels out so you end up with your answer.
The final answer is C. 45 seconds.
Step-by-step explanation:
It is given that, the total distance an object travels varies directly with the length of time it travels.
[tex]d\propto t[/tex]
If an object travels 32 meters in 18 seconds so,
[tex]32= 18k[/tex].....(1) (k is a constant)
If distance travelled is 80 meters, then the time taken is t say.
[tex]80= kt[/tex].....(2)
On solving equation (1) and (2), we get the value of t as,
t = 45 seconds
Hence, this is the required solution.
Which values of m and b will create a system of equations with no solution? Check all that apply.
y = mx + b
y = –2x + 3/2
[ ] m = –3 and b = -2/3
[ ] m = –2 and b = -1/3
[ ] m = 2 and b = -2/3
[ ] m = –3/2 and b = -2/3
[ ] m = –2 and b = -2/3
[ ] m = 3 and b = -2/3
Answers
After knowing this we can see that second and fifth option have m=-2 and they also have different coeficients. which means they are the answer
Answer is second and fifth option.
Answer: Answer is second and fifth option.
Step-by-step explanation:
m = –2 and b =
m = –2 and b =
What is the simplified form of 48 over 192??
Answers
Answer: The simplified form of 48 over 192 is 1 over 4.
Step-by-step explanation:
Since, A fraction is in its simplest form when the numerator and denominator cannot be any smaller, while still being whole numbers.
Also, for find the simplified form of a fraction,
We divide both numerator and denominator by their H.C.F,
Here, the given fraction is,
[tex]\frac{48}{192}[/tex]
Since, 48 = 2 × 2 × 2 × 2 × 3
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
H.C.F(48,192) = 2 × 2 × 2 × 2 × 3 = 48
[tex]\implies \frac{48/48}{192/48}=\frac{1}{4}[/tex]
Hence, The simplified form of 48/192 is 1/4.
The simplified form of 48/192 is 1/4.
First, let's find the GCD of 48 and 192.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The factors of 192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
The common factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
So, the greatest common divisor (GCD) of 48 and 192 is 48.
Now, we divide both the numerator and denominator by 48:
48/48 = 1
192/48 = 4
Therefore, the simplified form of 48/192 is 1/4.
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Which of the following is the solution set of -2|x| < -8
{x | -4 > x > 4} {x | -4 < x < 4} {x | x < -4 or x > 4}
Answers
divide both sides by -2, don't forget to flip sign
|x|>4
when you have
|a|>b
assume
a>b and a<-b is trrue
|x|>4
assume
x>4 and x<-4
last one is answer
What is the solution set of the following equation?
4/5x^2=2x-4/5
1. {1, 2}
2. {1, 1/2}
3. {2, 1\2}
Answers
4x^2=10x-4
divide both sides by 2
2x^2=5x-2
minus 5x from both sides and add 2 to both sides
2x^2-5x+2=0
use quadratic formula
for
ax^2+bx+c=0
x=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
given
2x^2-5x+2=0
a=2
b=-5
c=2
x=[tex] \frac{-(-5)+/- \sqrt{(-5)^2-4(2)(2)} }{2(2)} [/tex]
x=[tex] \frac{5+/- \sqrt{25-16} }{4} [/tex]
x=[tex] \frac{5+/- \sqrt{9} }{4} [/tex]
x=[tex] \frac{5+/- 3}{4} [/tex]
x=(5+3)/4 or (5-3)/4
x=8/4 or 2/4
x=2 or 1/2
3rd option is correct
Answer:
{2, 1\2}
Explanation:
What is equivalent to 3/4 (3y 15)?
Answers
The sum of three consecutive even integers is 66. Which equation represents the scenario?
Answers
consecutive even integers are 2 apart
they are x,x+2, and x+4
sum is 66
x+x+2+x+6=66
that is the equation
the answer is x=20, so the numbers are 20,22,24 if you were interested
The correct option is:
d. x + (x+2) + (x+4) = 66
The scenario involves three consecutive even integers. Let's denote the first even integer as x, the second one as x+2 (since it is the next consecutive even integer), and the third one as x+4 (as it is two more than the second one).
The sum of these three consecutive even integers is given to be 66. Therefore, the equation that represents this scenario is:
x + (x+2) + (x+4) = 66
So, the correct option is:
d. x + (x+2) + (x+4) = 66
The probable question may be:
The sum of three consecutive even integers is 66. Which equation represents the scenario?
a. x=66
b. x+(x+1)+(x+2)=66
c. x+x+x=66
d. x+(x+2)+(x+4)=66
The matrix C=[1,-2_-3,7] was used to encode a phrase to [7,-28,-25,-35,-2_-21,107,90,123,17]. Find C^-1 and use it to decode the matrix.
Answers
is the required matrix.
How many possible three-digit passwords can be formed using digits 0 through 9 if digits are repeated?
30 ,
720 ,
1,000 ...?
Answers
Answer:
The correct option is 3.
Step-by-step explanation:
Total digits 0 to 9 are
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Total number of digits is 10. It means total possible ways to select the first digit of the password is 10.
Since the reparation is allowed, therefore the possible ways to select the second and third digit of the password is 10.
Total possible ways to form a three-digit passwords is
[tex]10\times 10\times 10=1000[/tex]
Therefore the correct option is 3.
There are 1,000 possible three-digit passwords that can be formed using the digits 0 through 9 when repetition of digits is allowed, calculated as 10 possibilities for each of the three positions (10 x 10 x 10).
To determine how many possible three-digit passwords can be created using the digits 0 through 9 with repetition allowed, we consider each of the three positions in the password separately. For each position, we can use any of the 10 digits (0-9), leading to 10 possibilities for each digit.
Therefore, the total number of combinations for a three-digit password is:
First digit: 10 possibilities (0-9)Second digit: 10 possibilities (0-9)Third digit: 10 possibilities (0-9)By the rule of product, we multiply the possibilities for each digit:
10 imes 10 imes 10 = 1,000
Thus, there are 1,000 possible three-digit passwords when digits can be repeated.
DEFG Is a rectangle. DF=5x-5 and EG=x+11. find the value of x and the length of each diagonal. (Draw and label the sketch below) ...?
Answers
The two diagonals of a rectangle are equal. Thus,5x-5 = x+116x=16x = 8/3.
The length of the diagonal is thenDF = EG = 5x-5 = 5(8)/3 - 5 = 25/3 units.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
round 0.9874 to the greatest non zero place
Answers
0.9874~1.0
Is the square root of 100 rational or irrational?
What about the square root of 0.25?
Answers
Final answer:
The square root of 100 is rational, as is the square root of 0.25.
Explanation:
The square root of 100 is a rational number. A rational number is a number that can be expressed as a quotient or fraction of two integers, where the denominator is not zero. In this case, the square root of 100 is 10, which can be written as 10/1, making it a rational number.
The square root of 0.25 is also a rational number. The square root of 0.25 is 0.5, which can be expressed as 1/2, making it a rational number.
what is the purpose of a questionnaire
Answers
Answer:
It enables you to explore and know more
Step-by-step explanation:
Purpose Of Questionnaire
The main purpose of a questionnaire is to extract data from the respondents. It's a relatively inexpensive, quick, and efficient way of collecting large amount data even when the researcher isn't present to collect those responses first hand
What is the smallest angle of rotational symmetry for a square
Answers
When we rotate a figure and there is no change in the shape of the figure then it has rotational symmetry.
We know that the order of rotation for a square is 4.
Hence, we have [tex]\frac{360}{4} =90^{\circ}[/tex]
Thus, the angle of rotational symmetry of square are
[tex]90^{\circ}, 180^{\circ}, 270^{\circ}[/tex]
Hence, the minimum angle of rotational symmetry is [tex]90^{\circ}[/tex]
Therefore, the minimum angle of rotational symmetry for a square is 90 degrees.