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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https://brainly.com/question/20391090
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Answer:
Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
= 26
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Answer:
52 and 26
Step-by-step explanation:
2x=y
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3x=78
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To check:
52+26=78
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Answers
Answer:
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Step-by-step explanation:
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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!
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
See the image
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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To be clear, I am meaning in a format such as this;
456789098765432347898789
+ 567865676545678
----------------------------------------------
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Answer:
880 square meters
Step-by-step explanation:
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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.
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Learn more about area of rectangle here https://brainly.com/question/25292087
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
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Answers
Answer:
Well following the order of operations
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77/90 is the answer
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Answer:
no solutions
Step-by-step explanation:
-2+1=2+5
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Answer:
Yes
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
5 + 4 = 9
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Answer:
5/x+3+4/x+2=2
=9/x+5=2
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Answer x= -3
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4 friends and each wants 4 so total cookies
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Answer:
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Step-by-step explanation:
Expand by distributing terms
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Collect like terms.
(−7+6)+(−1.2x+8.8x)
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−1+7.6x
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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
a function is given, 2^x + 3. find f(-2)
Answers
Answer:
2_3_4_4/547767()9897568. thank