The figure below shows the graph of function f with domain [-1,1] and range [0,1].
![The Figure Below Shows The Graph Of Function F With Domain [-1,1] And Range [0,1].](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/DPtF4LkuPN5REv4EJg7IPc3PyebA0fR5.png)
Answers
The domain are the possible input while the range are the possible output
of a function.
(a) The domain = [-√2, √2], the range = [0, 2](b) The domain = [-1, 1], the range = [0, 1](c) The domain = [-1, 1], the range = [0, -1](d) The domain = [0, 2], the range = [0, 1](e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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Related Questions
If the smaller of two numbers is one-half of the larger number and the sum of the two numbers is 78, find the numbers
Answers
= 26
the numbers are 26 and 52
Answer:
52 and 26
Step-by-step explanation:
2x=y
x+y=78
3x=78
x=26
2(26)=y
y=52
To check:
52+26=78
string is 38 cm longer than his desk. Length of his reading book is 26 cm, what is the length of his string?
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Answer:
has in lenght of 2 or 5
Step-by-step explanation:
odyssey ware
ig i d k
Graph algebra problem! Can anybody help me out as graphs are definitely not my strong suit.
Answers
Answer:
f(2) = 5
Step-by-step explanation:
Definitions:Input values = x-coordinates.
The input values are also known as the domain, which is the set of all real numbers. With the domain of a function, you could substitute any real number into a given function for x and produce a valid output.Output values = y-coordinates
The range is the set of all real numbers that depend on the input values plugged into the function. Thus, the range represents the output (y-values) that corresponds to the input values used into the function. Function Notation:In the function notation f(x), f is the function name, and x is your input variable. Output values are also called functional values. You could use any letter to represent a function name, such as g(x), w(x), etc.,.Explanations:This particular question asks for you to identify the corresponding output (y-value) of the given input value, x = 2. If you look at the graph, the x-coordinate, x = 2, corresponds to the y-coordinate of 5.
Therefore, f(2) = 5.
Attached is an edited screenshot of the graph that you posted, where it shows where f(2) = 5 is located on the graph.
Answer:
f(2) = 5
Step-by-step explanation:
The 2 in f(2) means you're looking for the value of the function when x=2.
Find the vertical line that is the 2nd one to the right of the y-axis. Follow it up until you reach the function line (at the top edge of the graph). The y-value there is the value of f(2). That is 5 squares above the x-axis, so ...
f(2) = 5
Can someone help me please
Answers
Answer:
52.7%
Step-by-step explanation:
If I am correct it means to round the percentage, so it would be 58% if you are rounding it
12x3y2z3 - 8x2y2z2 + 20xy2z3
Answers
A corporation recently sold zero-coupon $400 bonds maturing in 4 years with an annual yield of 12%. Find the price. [Hint: The price is the present value of $400 4 years from now at the stated interest rate.] (Round your answer to the nearest cent.)
Answers
Answer:
Step-by-step explanation:
400*1.12^-4= 254.2072314
a function is given, 2^x + 3. find f(-2)
Answers
Answer:
2_3_4_4/547767()9897568. thank
The graph of a linear is shown below on the coordinate grid. What is the y-intercept of the graph of the linear equation? Bubble is your answer.
Answers
Answer: -7 on the y-axis
Step-by-step explanation:
Qiang is inviting 4 friends to a party each friend wants 4 cookies each box has 10 cookies how many boxes should qiang get
Answers
4 friends and each wants 4 so total cookies
required is 16. 1 box has 10 cooking which is not enough,
so you need to get 2 boxes to have more than
16 cookies
The question is in the pic! Answer by 10:20 to receive 5 stars, thanks, and brainliest!
please no links!
Answers
Answer:
A, y=1/3x
Step-by-step explanation:
You can use the slope formula.
I need to find out the answer for this problem...
Answers
Answer:
where is the problem to solve. please tell me
Need help on this plz and thanks
Answers
Answer:
y = 5x - 25
Step-by-step explanation:
Using the equation y=mx+b to determine the function. The line must be perpendicular, so the m (slope) value must be the opposite reciprocal of the given equation, which is 5. Then you have to solve the equation using the given point to find b.
10 = 5 * (7) + b
10 = 35 + b
-25 = b
So final equation is y = 5x - 25.
How many solutions −2(+1)=2+5
Answers
Answer:
no solutions
Step-by-step explanation:
-2+1=2+5
-1=7
-1 does not equal 7 so there are no solutions
paulita reads an average of 20 pages each day she has 6 days to read 10 pages will she finish her reading in 6 days explain?
Answers
Answer:
Yes
Step-by-step explanation:
If she is reading 20 pages a day, and needs to read 10 pages, then she needs half a day, and since she has 6 days, she can do this.
Hey, wassup its sofie dossi! I would like to ask you what 567865676545678+456789098765432347898789 is?
Answers
Answer:
828383627262827294688
Step-by-step explanation:
When you add 567865676545678 to 456789098765432347898789, the best way to do it is by placing the biggest number above the smallest number on a paper. Visual representation does help!
To be clear, I am meaning in a format such as this;
456789098765432347898789
+ 567865676545678
----------------------------------------------
Then, just as you would add any simple 2 number equation such as 3+5, etc. you will look at these numbers from right to left. Look at the bottom right one first, then add it to the one above it, if it adds up above 9, you will carry the leftover number above the row to the left of your current row. So currently you are in row 1, and you will add up to get 17. That means you will keep the 7 and write it down at the bottom and carry the one to the next row, and place it above the 8.
Hope this helps!
Eric ran 1 1/4 miles. Then he biked 3 1/2 times farther than he ran.
How far did Eric bike?
Enter your answer as a mixed number in simplest form.
Answers
Answer: He biked 4 and 3/8 miles
Step-by-step explanation:
since he ran 1.25 miles and biked 3.5 times farther than that you'd multiply both numbers and get 4.375 which simplifies to 4 and 3/8
help me ! ✬
work due tomorrow. i don’t understand this at all.
there’s 2 questions !
— don’t comment for points.
Answers
Answer:
32, 40
Step-by-step explanation:
See the image
Hope that helps! :)
On a coordinate grid, point L is at (−4, 4) and point S is at (8, 4). The distance (in units) between points L and S is ______. Input only whole numbers, such as 2.
Answers
Answer:
12 this is da a answer
12 twelve
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Answer:
way too long
Step-by-step explanation:
jk, 3 hours and 55 minutes
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Answers
Answer:
175% increase
Step-by-step explanation:
solve the equation 5/x+3 + 4/x+2 = 2
Answers
Answer:
5 + 4 = 9
x × x = X2
3 + 2 = 5
9/x + 5 = 2
Answer:
5/x+3+4/x+2=2
=9/x+5=2
9/x=-3
Multiply both sides by x
9= -3x
Divide by -3
Answer x= -3
Hope this helps
Please find the value of each of the variables. Show all work.
Answers
Answer:
W=20 V=42 X=87
Step-by-step explanation:
all sides are equal meaning that two corners from across each other are equal so v is 42 and w 20 this also means x is 87 im not too sure about y
The half-life of radium is 1690 years. If 80 grams are present now, how much will be present in 870 years?
grams
Answers
Answer:
A(t) = amount remaining in t years
= A0ekt, where A0 is the initial amount and k is a constant to be determined.
Since A(1690) = (1/2)A0 and A0 = 80,
we have 40 = 80e1690k
1/2 = e1690k
ln(1/2) = 1690k
k = -0.0004
So, A(t) = 80e-0.0004t
Therefore, A(430) = 80e-0.0004(430)
= 80e-0.172
≈ 67.4 g
Step-by-step explanation:
hope it helpful for you ❤️
-7+0.3(-4x+20)+8.8x
Help me plz
This is 8th grade math btw
Answers
Answer:
7.6x−1
Step-by-step explanation:
Expand by distributing terms
−7−1.2x+6+8.8x
Collect like terms.
(−7+6)+(−1.2x+8.8x)
Simplify
−1+7.6x
Regroup terms.
7.6x−1
Solve the following of:
11/15 × 7/8 ÷ 3/4
Answers
Answer:
Well following the order of operations
You just do this from left to right
11/15* 7/8 = 77/120
77/120 ÷ 3/4
or
77/120 * 4/3
77/90 (simplified)
77/90 is the answer
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Answers
Answer:
it is equal to 1.25
Step-by-step explanation:
hope it's helpful
Answer:
Decimal:
1.25
Mix Number:
1 1/4
Improper Fraction:
5/4
Step-by-step explanation:
10/8 is 1.25
In fraction it is 1 1/4 or 5/4
Hope this helps!
expression:
x + 20 + x + 20 + x + 20 + x + 20
Answers
Answer: if is simplify the answer is 4x+80
Step-by-step explanation:
How to determine the domain and range of a continuous graph
Answers
Answer:
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
A rectangular board is 1100 millimeters long and 800 millimeters wide. What is the area of the board in square meters? Do not round
Answers
Answer:
880 square meters
Step-by-step explanation:
You need to find the area of the rectangular board, which would be 1100x800=880000 square millimeters. 1 meter=1000 millimeters, so you divide 880000 by 1000, getting 880 square meters.
The area of the board is 880 square meters.
Area of rectangleYou need to find the area of the rectangular board, which would be 1100x800=880000 square millimeters.
1 meter=1000 millimeters, so you divide 880000 by 1000, getting 880 square meters.
Learn more about area of rectangle here https://brainly.com/question/25292087
#SPJ2
Which transformations map the strip pattern onto itself?
PPPPP
O
a horizontal translation only
a horizontal translation and a glide reflection
a horizontal translation and a reflection across a vertical line
a horizontal translation and a 180° rotation
Answers
Answer:
2nd is correct
But u can also write by guessing. it is the best trick used by toppers.