Consider function f.
Which statement is true about function f?
A.
The function is continuous.
B.
As x approaches positive infinity, approaches positive infinity.
C.
The function is increasing over its entire domain.
D.
The domain is all real numbers.
Answers
Answer:
Step-by-step explanation:
Check for continuity by evaluating 2^x and -x^2 - 4x + 1 at the break point x = 0: 2^0 is 1 and -x^2 - 4x + 1 is also 1, so these two functions approach the same value as x approaches 0.
Now do the same thing with
-x^2 - 4x + 1 and (1/2)x + 3 at x = 2; the first comes out to -11 and the second to 4. Thus, this function is not continuous at x = 2.
We must reject statement A.
Statement B: as x increases without bound, (1/2)x + 3 also increases without bound. This statement is true.
Statement C: False, because the quadratic -x^2 - 4x + 1 has a maximum at
x = -b/[2a], or x = -(-4)/[-2], or x = -2
Statement D: True: there are no limitations on the values of the input, x.
The statement B is as x approaches positive infinity f(x) approaches positive infinity is true
What is the definition of the limit?A point or level beyond which something does not or may not extend or pass.
We have to check for continuity by evaluating [tex]2^x[/tex] and [tex]-x^2 - 4x + 1[/tex]
at the break point x = 0
[tex]2^0[/tex]is 1 and [tex]-x^2 - 4x + 1[/tex] is also 1,
So these two functions approach the same value as x approaches 0.
Now do the same thing with
[tex]-x^2 - 4x + 1[/tex]and [tex](1/2)x + 3[/tex] at x = 2;
The first comes out to -11 and the second to 4.
Thus, this function is not continuous at x = 2.
We must reject statement A.
for B we have as x increases without bound,
[tex](1/2)x + 3[/tex]
also increases without bound.
Therefore the statement B is true statement.
Statement C is False,
because the quadratic[tex]-x^2 - 4x + 1[/tex] has a maximum at
[tex]x = -b/[2a],[/tex]
[tex]x = -(-4)/[-2],[/tex]
[tex]x=-2[/tex]
There are no limitations on the values of the input, x.
D is also false negative number are in real numbers.
Therefore,the statement B is as x approaches positive infinity f(x) approaches positive infinity is true
To learn more about the limit visit:
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Related Questions
20 points help i dont get my brothes school work LOL
Answers
Answer:
1/12 a mile
Step-by-step explanation:
Answer:
B. 1/12 is the right answer because you have to times the fraction by the reciprocal because you can't divide a fraction. So, you do 1/3 *1/4 = 1/12
Step-by-step explanation:
have a good day/night
may i please have a branlliest
If each serving of the stew will contain 1 4 14 pound of meat, how many servings of the stew can the club make? Enter your answer in the box.
Answers
Complete question :
The line plot shows the weights of packages of meat that members of a club bought. The meat will be mixed with vegetables to make stew for a club dinner. Each serving of the stew contains 1/4 pound of meat. How many servings of the stew can the club make?
Answer:
36 servings
Step-by-step explanation:
From the plot ; we take the sum of total weight of meat packages :
(5/8 * 2) + 6/8 + 1 + (9/8 * 3) + 10/8 + 11/8
10/8 + 6/8 + 8/8 + 27/8 + 10/8 + 11/8 = 72 / 8 = 9 meat packages
Each serving of meat = 1/4
Number of servings the club can make :
Total meat package / pound of meat per serving
(9 ÷ 1/4)
9 * 4/1
= 36 servings
Answer:
36 hope this help
Step-by-step explanation:
A cylinder has a height of 17 inches and a radius of 8 inches what is the use π = 3.14 and round your answer to the nearest hundredth
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Answer:
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Step-by-step explanation:
what inequality is equivalent to 2/3x - 5 <11 ?
Answers
given a is equal to 60 degree and 30 degree prove that sin a + b is equal to sin a cos b + cos a sin b
Answers
Answer:
A = 60 and B = 30
Now, A + B = 60 + 30 = 90
Also, A – B = 60 – 30 = 30
sin (A + B) = sin 90 = 1
sin A cos B + cos A sin B = sin 60 cos 30 + cos 60 sin 30
Consider this right triangle...
Omg pleaseeeee help me!! I have SBA Math Test on Friday and I forgot everything I learned last year from Geo. Help would be very very much appreciated!! WILL GIVE BRAINLIEST!! Thank you so muchhhhh <3
Answers
Answer:
33°
Step-by-step explanation:
have a nice day!! :)
Last month a bakery sold a total of 3,500 cookies and cupcakes. They sold cookies for $0.75 each and cupcakes for $2 each. If the total sales last month was $4,500, how many cookies and how many cupcakes did the bakery sell?
Answers
Answer:
Number of cookies sold is 2000 and number of cupcakes sold is 1500
Step-by-step explanation:
Let number of cookies be [tex]x[/tex]
and number of cupcakes be [tex]y[/tex] so
[tex]x+y=3500[/tex]
Cost of one cookie is $0.75
Cost of one cupcake is $2
[tex]0.75x+2y=4500[/tex]
[tex]x+y=3500[/tex] [tex]\times 2[/tex]
[tex]2x+2y=7000[/tex]
[tex]-1.25x=-2500\\\Rightarrow x=\dfrac{2500}{1.25}\\\Rightarrow x=2000[/tex]
[tex]y=3500-x=3500-2000\\\Rightarrow y=1500[/tex]
Number of cookies sold is 2000 and number of cupcakes sold is 1500.
What is the probability of landing on a 9 and then landing on a 7?
Answers
Answer:
what are we landing on? D 10s D20s?...
Step-by-step explanation:
:/
Expand and simplify 3(2x-y)-2(4x-2y)
Answers
What is the solution to follow system of equations?
x-3y=7
2x-6y=12
Answers
Please answer correctly !!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
What is the measure of the missing angle?
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Answer:
42
Step-by-step explanation:
Hello, I need help! The question is "Today you will look over the following problem that Nancy worked and explain what she did incorrectly and why it does not work. Then tell me what information Nancy would need to know in order to use this theorem correctly"
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Answer:
Step-by-step explanation:
Remark
The ratios are certainly correct but that doesn't mean that they show similarity. SSA is a very dangerous proposition to use. Redraw triangle DEF of that DF is going to upwards to your right hand side. Make E as it was before. Why isn't this right?
It isn't right because E has gone from being an acute angle to an obtuse angle (an angle larger than 90 but less than 180).
The ratios are still true, but the angles do not match. So the whole answer is incorrect.
Select the correct answer
Answers
Answer:
x = 95°
y = 147°
z = 128°
Step-by-step explanation:
z = 180 - 52 = 128°
x: first find the remaining angle in the big triangle, 180 - (45 + 50) = 85°
x = 180 - 85 = 95°
y: first find the remaining angle in the small triangle, 180 - (95 + 52) = 33°
y = 180 - 33 = 147°
Does anyone know which answer it is in the image? Doesn’t require any work
Answers
Answer:
b
Step-by-step explanation:
Answer:
It's the second one
A submarine started 30 feet below the surface of the water. It is now 10 feet below the surface. What integer represents the change in depth?
Answers
Answer:
-20 feet
Step-by-step explanation:
change in depth = number of feet below the surface + number of depth on the surface
Because the submarine is below surface, a value of -30 would be given
-30 + 10 = -20 feet
3. A circle with center (0,0) has a y-intercept at (3,0).
Find the equation of the circle.
Answers
Answer:
x^2 + y^2 = 9
Step-by-step explanation:
The standard equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2. Here h = 0, k = 0, x = 3 and y = 0:
(3 - 0)^2 + (0 - 0)^2 = r^2, or
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The equation of this circle is (x - 0)^2 + (y - 0)^2 = 9, or
x^2 + y^2 = 9
Two number cubes with sides numbered 1-6 are rolled. What is the probability that the sum of the numbers on the cubes is 12?
Answers
Answer:
1/36
Step-by-step explanation:
Attached is a chart showing the 36 possible outcomes for rolling 2 number cubes. The sum of the two cubes is 12 in only one of the outcomes (both sixes). The probability is 1/36.
help
What is the domain and range of the exponential graphed below?
A.Domain: All real numbers
Range: y > -4
B.Domain: All real numbers
Range: All real numbers
C.Domain: x > 0
Range: y < -6
D. Domain: All real numbers
Range: y > 0
Answers
Answer:
B
Step-by-step explanation:
I just did the test
The range and domain of the function exists on all real values
Domain and Range of functionsDomain of a function is the value of the input of graph for which the function exists.
The range of a function is the value of the output of graph for which the function exists.
The given graph denotes an exponential function showing the arrow pointing infinitely in both directions. Hence the range and domain of the function exists on all real values
Learn more on range and domain here: https://brainly.com/question/2264373
Find the discriminant of the following quadratic equation then state the number of rational, irrational, and imaginary solutions.
Equation: −6x2−6=−7x−9
Discriminant: Answer
Solutions:
Answers
Answer:
-6x² - 6 = -7x - 9-6x² + 7x - 6 + 9 = 0-6x² + 7x + 3 = 06x² - 7x - 3 = 0Discriminant:
D = (-7)² - 4*6*(-3) = 49 + 72 = 121Since D > 0, there are 2 real solutions:
x = (- (-7) ±√121 )/12x = (7 ± 11)/12x = 1.5, x = -1/3solve the equation-4(x+10)-6=-3(x-2)
Answers
Answer: x= -52
Step-by-step explanation:
Will give brainiest help please
Write the equation of the line in Slope-Intercept Form.
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bakit mahalagang matutunan ang mga angkop na pahayag sa panimula gitna at wakas mg isang akda
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Answer:
i understand your statement my good sir but, what is the question?
Step-by-step explanation:
1. Find the area of each circle. Use 3.14 for A. Round to the nearest tenth.
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RE
Answers
Answer:
78.5 cm²Step-by-step explanation:
Area of circle:
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How many units long is the perimeter of the rectangle?
Answers
10 + 10 + 6 + 6 = 32
The required perimeter of the rectangle is 28 units.
What is a rectangle?
The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
Let's denote the length of the rectangle as L and the width as W. We know that the diagonal of the rectangle has a length of 10 units, and we can use the Pythagorean theorem to relate the length, width, and diagonal,
L² + W² = diagonal² [= 10² = 100]
We also know that one side of the rectangle has a length of 6 units, which we can assume is the width W. Therefore, we can solve for the length L,
L² + 6² = 100
L² = 100 - 36
L² = 64
L = 8
So the length of the rectangle is 8 units.
To find the perimeter of the rectangle, we can use the formula P = 2L + 2W, where L is the length and W is the width:
P = 2(8) + 2(6)
P = 16 + 12
P = 28
Therefore, the perimeter of the rectangle is 28 units.
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#SPJ2
An 80–calorie apple is 4% of jeremy’s daily caloric intake. What is Jeremy’s daily caloric intake?
Answers
Answer:
3.2 calories
Step-by-step explanation:
4% is .04
so
80 x .04 = 3.20
Megan has $45.12 in her purse. She spends $7.89 for lunch and $21.25 for a pair of sunglasses.
Which is the best estimate for the amount of money Megan has left?
Answers
Answer:
Hello Love!
A good estimate would be 15 or 16 dollars left
Hope this helps!
Answer:
$15.98
Step-by-step explanation:
45.12-7.89=37.23
37.23-21.25=15.98
a bowling ball with a diameter of 10.9
Answers
Answer:
34.226
Step-by-step explanation:
10.9 ÷ 2 = 5.45
C = 2πr
2 × 5.45 × 3.14
34.226
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Answers
Match the function with the graph
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Have a good day!