What is the range of the function f(x) = |x − 1| − 2?all real numbersall real numbers less than or equal to −2all real numbers less than or equal to 1all real numbers greater than or equal to −2?
Answers
.. all real numbers greater than or equal to -2 . . . . the last selection
The range of the function f(x) = |x - 1| - 2 is all real numbers greater than or equal to -2.
Explanation:The function f(x) = |x - 1| - 2 represents the absolute value of x minus 1, subtracted by 2.
The range of the function can be determined by finding the minimum and maximum values it can take.
Since the absolute value of a number is always greater than or equal to zero, the lowest value that f(x) can take is when |x - 1| = 0, which happens when x = 1.
Therefore, the minimum value of f(x) is -2.
As x increases or decreases from 1, the value of f(x) increases.
So, there is no upper bound for the range of f(x).
Therefore, the range of the function is all real numbers greater than or equal to -2.
Related Questions
Which trigonometric function is equivalent to sec(-270) ? a. sec(-120) c. sec(-30) b. sec(60) d. sec(90)
Answers
we add our angle to 360°
-270+360
=90
But sec(-270) is a positive value, this implies that the angle that will give us the same answer as sec (-270) should also give us the positive value. This means that 90 is our answer since it will give us the positive sec value.
The answer is d. sec(90)
Answer: d
Step-by-step explanation: edge 2021
One angle of atriangle measures 12 degrees. the second angle's measurements is five times the third. what is the measure of the third angle
Answers
The measure of the third angle is; 28 degrees.
How does an angle form?An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.
The point of their joint is called vertex of that angle.
Those two line segments forming it are called arms of that angle.
The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.
Let the third angle be x
Given that One angle of a triangle measures 12 degrees. the second angle's measurements is five times the third.
We know that in a triangle the angles add up to 180 degrees.
so, 12 + 5x + x = 180.
Then we get
6x =168
x =28 degrees.
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Two angle measures in a scaled Triangle are 77 and 62 what is the measure of the third angle
Answers
We know that the sum of all 3 angles in a triangle is 180°
Two angles are given to be 77° and 62°
We can find the 3rd angle by:
77 + 62 + x = 180 ( x is the angle to be found, you can use any variable, if not given)
180 - ( 77 + 62 ) = x
180 - 138 = x
41°
Two competing cable companies have recently restructured their payment plans. Clear TV requires a $30 activation fee and charges $75 per month for their basic plan. Link TV requires no activation fee and charges $82.50 per month for their basic plan. When will the two plans be equal in cost?
Answers
Activation fee = $30
Monthly charge = $7
Link TV:
Activation fee = $0
Monthly Charge = $82.50
Let x be the number of month that the two cost will be equal
30 + 75x = 82.5x
82.5x - 75x = 30
7.5x = 30
x = 30 ÷ 7.5 = 4 months
The two plans will be of equal cost after 4 months.
the square root of 2.25 is _____. 15 1.5 0.15 irrational
Answers
Answer:
The square root of 2.25 is 1.5.
Step-by-step explanation:
We have been given an incomplete sentence. We are asked to bill in the given for our given sentence and complete it.
The square root of 2.25 is _____.
Let us find [tex]\sqrt{2.25}[/tex].
[tex]\sqrt{2.25}=1.5[/tex]
Therefore, the square root of 2.25 is 1.5 and option B is the correct choice.
Roasting meats at high temperatures makes them moist and tender.
True False
Answers
Answer:
False
Step-by-step explanation:
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PLEASE GET THIS RIGHT!!!!!!!! The difference between 3.6 and a number is 2.95, as shown below. What number should go in the box to complete the subtraction problem?
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3.60
- 0.65
---------------
2. 9 5
what are the four main ideas of physical science,
Answers
what is the solution of this equation x + 6 =24
Answers
x=18
Find the length of the side labeled x round to the nearest 10th
Answers
Cos. 25 = y/44
Cos. 25 x 44 = y
0.9063 x 44 = y
39.8772 = y
Now that we have the altitude you can set up another equation for x.
Tan. 34 = x/39.8772
Tan. 34 x 39.8772 = x
0.6745 x 39.8772 = x
26.8971714 = x
Final Answer: x is approximately 26.9
Using complete sentences, explain the key features of the graph of the sine function.
Answers
List the coordinates of the image after a rotation of the figure below of 180° about the origin. 20 points
(__ , __)
(__ , __)
(__ , __)
(__ , __)
Find the measures of the segment and its image:
AD = √___, A'D' = √___
Answers
B' (-5,-4)
C' (-7,-2)
D' (-4,0)
AD = sqrt(2)
A'D' = sqrt(2)
Answer: The co-ordinates of the image quadrilateral areA'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
Step-by-step explanation: We are given to list the co-ordinates of the image after a rotation of the figure below of 180° about the origin.
From the figure, we note that
the co-ordinates of the vertices of quadrilateral ABCD are A(3, 1), B(5, 4), C(7, 2) and D(4, 0).
We know that
the co-ordinates of the image of a point (x, y) after rotation of 180° about the origin is given by (-x, -y).
Therefore, after rotating the quadrilateral ABCD through an angle of 180° about the origin, then the co-ordinates of the image A'B'C'D' are
A(3, 1) ⇒ A'(-3, -1),
B(5, 4) ⇒ B'(-5, -4),
C(7, 2) ⇒ C'(-7, -2)
and
D(4, 0) ⇒ D'(-4, 0).
And, the lengths of the line segments AD and A'D' can be calculated using distance formula as follows :
[tex]AD=\sqrt{(4-3)^2+(0-1)^2}=\sqrt{1+1}=\sqrt{2}~\textup{units},\\\\A'D'=\sqrt{(-4+3)^2+(0+1)^2}=\sqrt{1+1}=\sqrt 2~\textup{units}.[/tex]
Thus, the co-ordinates of the image quadrilateral are A'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
A ball is thrown straight up with a initial velocity of 56 feet per second . The height , h , of the ball t seconds after it is thrown is given by the formula h(t)=56t-16t^2 . What is the maximum height of the ball?
Answers
Formula: H(t) = 56t – 16t^2
H(t) = - 16t^2 + 56t
A. What is the height of the ball after 1 second? H (1) = 56(1) – 16(1) ^2 = 40 pt.
B. What is the maximum height? X = - (56)/2(- 16) = 1.75 sec h (1.75) = 56(1.75) – 16(1.75) ^2 h (1.75) = 49ft.
C. After how many seconds will it return to the ground? – 16t^2 + 56t = 0 - 8t =0 t = 0
- 8t (2 + - 7) = 0 2t – 7 = 0 t = 7/2 Ans: 3.5 seconds
The maximum height achieved by the ball is 49 meters at time t = 7/4 seconds.
What is time dependent function?
The time dependent function is the function whose values vary with change in time. For example - f(t) = 3t + 5.
Given is a ball is thrown straight up with a initial velocity of 56 ft/s. The height (h) , of the ball (t) seconds after it is thrown is given by the formula h(t) = 56t - 16t²
The given function is -
h[t] = 56t - 16t²
Now, for maximum height -
dh/dt = 0
d/dt ( 56t - 16t²) = 0
d/dt (56t) - d/dt (16t²) = 0
56 - 16 d/dt (t²) = 0
56 - 16 x 2t = 0
56 = 32t
t = 56/32
t = 7/4 seconds
Now, at t = 7/4 seconds, the height is maximum. Substituting the value
t = 7/4 seconds, we get -
h(7/4) = 56 x 7/4 - 16 x 49/16
h(7/4) = 14 x 7 - 49
h(7/4) = 98 - 49
h(7/4) = 49 meters
Therefore, the maximum height achieved by the ball is 49 meters at time t = 7/4 seconds.
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There are three consecutive odd integers. Three times the largest is seven times the smallest. What are the integers?
Answers
This is how I would map out this problem...
First I would represent the smallest integer with the variable x. Since they are consecutive odd integers, add 2 to the middle integer and add 4 to the largest.
smallest: x
middle: x+2
largest: x+4
Now we need to find a way to solve for x. Since 3 times the largest is 7 times the smallest, we can set up an equation like this...
3(x+4)=7x
Now solve it!
3(x+4)=7x
3x+12=7x
12=4x
x=3
Now let's go back to our original data...
smallest: x
•Since the smallest is x, that means the smallest is going to be 3.
middle: x+2
•since the middle one is x+2, plug in 3 for x and we get 5.
largest: x+4
•since the largest is x+4, plug in 3 for x and we get 7.
This means the answer is...
Smallest: 3
Middle: 5
Largest: 7
I really hope this helps!
Best wishes :)
The time it takes runners to complete a certain marathon are normally distributed with a mean of 4.6 hours and a standard deviation of 1.1 hours what is the time for a runner with a score of -1.2? Round to the nearest hundredth
Answers
The equation for the z-score is
z-Score = (Time - Mean) / Standard Deviation
Given:
mean = 4.6 hours
standard deviation = 1.1 hours
z-Score = -1.2
∴ -1.2 = (x - 4.6) / 1.1
x - 4.6 = -1.32
x = 3.28 hours
The time would be 3.28 hours for a z-score of -1.2.
Explanation:
The formula for a z-score is
z = (X-μ)/σ,
where μ is the mean and σ is the standard deviation.
For our problem, we know that z = -1.2, μ = 4.6 and σ = 1.1:
-1.2 = (X-4.6)/1.1
Multiply both sides by 1.1:
-1.2(1.1) = ((X-4.6)/1.1)*1.1
-1.32 = X-4.6
Add 4.6 to both sides:
-1.32+4.6 = X-4.6+4.6
3.28 = X
Spaceship Earth, a major tourist attraction, is a sphere whose diameter is approximately 50 m. What is the volume of Spaceship Earth? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest hundredth.
Answers
volume of a sphere=(4/3)*pi*r³
diameter= 50 m--------------> r=D/2--------> r=25 m
Volume=(4/3)*pi*25³------------> volume=65416.666 m³
the answer is 65416.67 m³
Deeside weather the given number is a solution of the given equation. Is 8 a solution of y + 9 = 17? Yes or no.
Simplify the expression by combining like terms. 10x - x - 2x - x
8x
x² + 8x
6x
-x² + 8x
Answers
Porters family ordered 4 pizzas. They ate 2 3/8 of pizza how much pizza is left?
Answers
Someone help me ASAP!!!!!!
Answers
The points are (7.5, 0) and (0, -5)
help please!!!
In Angle ABC, C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
a = 3, c = 19
A. M
B. M
C. M
D M
Answers
19^2 = 3^2 + b^2
b = (361 - 9)^1/2 = 18.761663039294
Now for angles
sin(A) = a/c = 3/19
A = sin{-1}(3/19) = 9.0847202873911
A = 9.0847202873911
sin(B) = b/c = 18.761663039294 / 19
B = sin{-1}(18.761663039294 / 19) = 80.915279712614
B = 80.915279712614
PLEASE HELP ME WITH THIS QUESTION AND DON'T FORGET TO EXPLAIN
Answers
All the functions given in the options are linear functions in the form y=mx+b, then we must find a function with independent term (y-intercept) b=690
The functions with b=690 are the first and third option.
For the slope (m), we can calculate it with 2 points of the table:
n1=0, d(n1)=690
n2=2, d(n2)=560
m=[d(n2)-d(n1)] / (n2-n1)
m=(560-690) / (2-0)
m= (-130) / 2
m=-65
Then the function must be:
d(n)=mn+b, m=-65, b=690
d(n)=-65n+690
Answer: Third option d(n)=-65n+690
1/3 math questions. pls help! 20 pts!
Answers
8 × 1 = 8
8 × 2 = 16
The actual length of the trail is 16km.
Hope this helps!
John let out 50 foot of kite string when he observes that his kite is directly above a point on the ground 30 feet away from him, how high is the kite ?
Answers
Answer:
the answer is 40 i had it on USATestPrep
Step-by-step explanation:
ion need one lml
In the right triangle shown, AC = BC = 7? What is AB?
Answers
BC=2.7cm, AC=1.1cm, B wrong
How use zero product property to solve equations
Answers
In words: if two numbers multiply to 0, then one (or both) of the values must be zero.
So in terms of algebra, if we had
-0.2*(x-1.9)*(x-3.5) = 0
then
x-1.9 = 0 or x-3.5 = 0
Now solve each individual equation for x
x-1.9 = 0
x-1.9+1.9 = 0+1.9 ... adding 1.9 to both sides
x = 1.9
x-3.5 = 0
x-3.5+3.5 = 0+3.5 .... adding 3.5 to both sides
x = 3.5
The two solutions are x = 1.9 or x = 3.5
These two x values, when plugged into f(x), will make f(x) = 0
These are the x intercepts because this is where the graph crosses the x axis.
Note: "root" is another term for "x intercept"
explanation and answer
Answers
h/4 = 12/h
h^2 = 48
h = 6.93
19)
x/ 12 = 3/x
x^2 = 36
x = 6
y^2 = 144 - 36
y^2 = 108
y = 10.39
A ball is thrown into the air from the edge of a 48 foot cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.
For which interval is the ball’s height always decreasing?
A. 48
B.0
C.2.5
D.146
Answers
2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
What is time interval?" Time interval is the division of time into small equal intervals to have a proper observation of any data."
According to the given graph,
x represents time in seconds along x-axis
y represents height in foot of the ball along y-axis
As per observation,
Height of the ball increasing from 48 to 146 in the time interval
0< x < 2.5.
Height of the ball decreasing from 146 to 0 in the time interval 2.5< x < 5.5.
Hence, we conclude that 2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
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Dimension of triangle A are three times the dimensions of triangle
b. The area of triangle A is 252 cm squared. What is the area of triangle B?
Answers
Answer:
28 cm2
Step-by-step explanation:
I did this question
What is the solution of the equation x2 + 10x + 75 = 0?
Answers
[tex]x = - \frac{77}{10} [/tex]
alternative form
[tex]x = - 7 \frac{7}{10} \: \: x = - 7.7[/tex]
x = [- b +/- sqrt( b^2 - 4ac ) ] / 2a
a = 1
b = 10
c = 75
x = [ -10 +/- sqrt(-200)]/2
x = [ -10 +/- 10 sqrt(2) / 2
x = - 5 + / - 5 sqrt(2) and that's your answer.
PLEASE HELP ME ON THIS QUESTION
THX~ BRANiLiEST AVAILABLE
PLZ EXPLAIN IF U COULD
Answers
D's answer shows that the graph is only increasing by 1/2, and C shows that the graph will increase at a normal rate.
The answer is C.