The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of functio
n g(x). Which statements about the functions f(x) and g(x) are true? Check all that apply. The functions have the same range. The functions have the same domains. The only value that is in the domains of both functions is 0. There are no values that are in the ranges of both functions. The domain of g(x) is all values greater than or equal to 0. The range of g(x) is all values less than or equal to 0.'
2 answers:
Answer:
The true statements:
The only value that is in the domains of both functions is 0.
The range of g(x) is all values less than or equal to 0.
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Step-by-step explanation:
See the attached figure:
As shown: f(x) = √x with blue color
When f(x) is reflected across the x-axis the result will be (-√x) with red color.
Then the is reflected result across the y-axis to create the graph of function g(x) = -√(-x) with green color.
<u>Domain </u>of f(x) = [0,∞) & <u>Range</u> of f(x) = [0,∞)
<u>Domain </u>of g(x) = (-∞,0] & <u>Range </u>of g(x) = (-∞,0]
So, according to previous, we will check the statements:
1) The functions have the same range. <u>(Wrong)</u>
2) The functions have the same domains. <u>(Wrong)</u>
3) The only value that is in the domains of both functions is 0. <u>(True)</u>
4) There are no values that are in the ranges of both functions. <u>(Wrong)</u>
5) The domain of g(x) is all values greater than or equal to 0. <u>(Wrong)</u>
6) The range of g(x) is all values less than or equal to 0. <u>(True)</u>
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Answer:
The explanations for the graphs are provided down below. Please let me know if you have any questions about my answer.
12 and 13 as written on the worksheet is right.
Step-by-step explanation:
12) The answer given is correct.
The relation between x and y is given as:
with
.
I replaced the word domain with x since the domain is the set of x's for which the relation exists.
We are going to replace x with each of the x's given to see what y corresponds to each.
Let's begin with x=-4.
with
:
.
So (-4,5) is an ordered pair that should be on our graph.
To find this point you move left 4 from origin then up 5. Now you put a dot where you have landed. Your graph does show this point.
Moving on.
Let's do the next x: x=-2.
with
:
.
So (-2,-1) is an ordered pair that should be on our graph.
To find this point you move left 2 from origin and then down 1. Now you put a dot where you have landed. Your graph shows this point as well.
Now x=0.
with
:
So (0,-3) is an ordered pair that should be on our graph.
To find this point you move left and right none and down 3. Now you put a dot where you have landed. Your graph shows this point.
Now the last point will be at x=2.
with
.
So (2,-1) is an ordered pair that should be on our graph.
To find this point you move 2 units right from the origin and then down 1 unit. Now put a dot where you landed. The graph shows this point as well.
13) The answer given is correct.
is the parent function and makes like a V shaped graph where it's vertex is at (0,0).
If we want to move this graph right 3 it becomes:
.
If you move that up once it becomes:
or
which is the curve given.
If you don't know about transformations you can choose a few points to plug in to see what's going on with the graph.
Let's choose x=-5,-3,-1,0,1,3,5.
x=-5
f(-5)=|3--5|+1=|3+5|+1=|8|+1=8+1=9.
There is no room for (-5,9) on our graph but if you extended the left hand side of the absolute value function there you would see that (-5,9) is reached.
x=-3
f(-3)=|3--3|+1=|3+3|+1=|6|+1=6+1=7.
(-3,7) should be a point on the graph. Same thing for this point as (-5,9).
x=-1
f(-1)=|3--1|+1=|3+1|+1=|4|+1=4+1=5.
(-1,5) is located on the graph.
x=0
f(0)=|3-0|+1=|3|+1=3+1=4.
(0,4) is also located on the graph.
x=1
f(1)=|3-1|+1=|2|+1=2+1=3.
(1,3) is located on the graph.
x=3
f(3)=|3-3|+1=|0|+1=0+1=1.
(3,1) is located on the graph.
x=5
f(5)=|3-5|+1=|-2|+1=2+1=3.
(5,3) is located on the graph.
Now if we weren't given the graph already:
I would plot the points I found which were:
(-5,9)
(-3,7)
(-1,5)
(0,4)
(1,3)
(3,1)
(5,3)
We should get a basic idea of what the function looks like from these points.
I will graph them. You will have to connect these points because the domain isn't discrete like number 12 is. That is they didn't list out elements for the domain.
I'm going to graph one more point after x=5.
How about x=7?
So (7,5) is also a point on the graph.
You should see that the blue points are following the red path I made there.
Answer:
r=1/π
Step-by-step explanation:
Area of the circle is defined as:
Area = πr²
Derivating both sides
=2πr
=
x
= 2πr
If area of an expanding circle is increasing twice as fast as its radius in linear units. then we have : =2
Therefore,
2πr = 2
r=1/π