The function g(x) = 8(4x) is reflected across the x-axis to create f(x). What is the equation for f(x)? f(x) =_____ (4)x
2 answers:
Answer:
Step-by-step explanation:
The transformation that reflects the function on the axis is:
.
Therefore if we have the function
and we call
to the transformation that relieves g (x) on the x axis then:
Finally the equation for f(x) es:
Answer:
f(x) = -8(4)x
Step-by-step explanation:
The reflection of the point (x,y) across the x-axis is the point (x,-y).
Having said this, to reflect the function y=g(x) = 8(4x) over the x-axis, we just need to evaluate the equation in the point: (x,-y).
y = 8(4x) ⇒ -y = 8(4x) ⇒ y = -8(4x)
Then f(x) = -8(4x)
Attached you will find the graph of g(x) (blue) and f(x) (red),
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<em><u>Answer:</u></em>
MN = 4 units
<u><em>Explanation:</em></u>
<u>1- getting the value of m:</u>
<u>We are given that:</u>
NQ = 4m and NQ = 12
<u>This means that:</u>
12 = 4m
m = 3
<u>2- getting MQ:</u>
<u>We are given that:</u>
MQ = 5m + 1
<u>We have calculated that:</u>
m = 3
<u>Therefore:</u>
MQ = 5(3) + 1 = 15 + 1 = 16 units
<u>3- getting MN:</u>
We are given that point N is located somewhere between points M and Q.
<u>This means that:</u>
line MQ can be divided into two portions: MN and NQ
<u>This also means that:</u>
length of MQ = length of MN + length of NQ
<u>We have calculated that:</u>
MQ = 16 units
<u>We are given that:</u>
NQ = 12 units
<u>Therefore:</u>
16 = length of MN + 12
length of MN = 16 - 12
length of MN = 4 units
Hope this helps :)
MN = 4 units
<u><em>Explanation:</em></u>
<u>1- getting the value of m:</u>
<u>We are given that:</u>
NQ = 4m and NQ = 12
<u>This means that:</u>
12 = 4m
m = 3
<u>2- getting MQ:</u>
<u>We are given that:</u>
MQ = 5m + 1
<u>We have calculated that:</u>
m = 3
<u>Therefore:</u>
MQ = 5(3) + 1 = 15 + 1 = 16 units
<u>3- getting MN:</u>
We are given that point N is located somewhere between points M and Q.
<u>This means that:</u>
line MQ can be divided into two portions: MN and NQ
<u>This also means that:</u>
length of MQ = length of MN + length of NQ
<u>We have calculated that:</u>
MQ = 16 units
<u>We are given that:</u>
NQ = 12 units
<u>Therefore:</u>
16 = length of MN + 12
length of MN = 16 - 12
length of MN = 4 units
Hope this helps :)
Answer:
y 0 1 2 3
P(Y=y) 0.0676 0.3549 0.3875 0.19
Step-by-step explanation:
P(Wed) = 0.26
P(Thurs) = 0.39
P(Fri) = 0.25
P(Sat) = 0.10
Y = No. of days beyond Wednesday it takes for both magazines to arrive i.e. 0,1,2,3
Y=0 means the magazines will arrive on Wednesday
Y=1 means the magazines will arrive till Thursday
Y=2 means the magazines will arrive till Friday
Y=3 means the magazines will arrive till Saturday
The possible combinations for Y are
Y(W,W) Y(W,T) Y(W,F) Y(W,S)
Y(T,W) Y(T,T) Y(T,F) Y(T,S)
Y(F,W) Y(F,T) Y(F,F) Y(F,S)
Y(S,W) Y(S,T) Y(S,F) Y(S,S)
So, we can classify these possible outcomes as Y=0,1,2,3.
Y(0) = Y(W,W) (both magazines take 0 days to arrive beyond Wednesday)
Y(1) = Y(W,T), Y(T,T), Y(T,W) (both magazines take 1 day to arrive beyond Wednesday)
Y(2) = Y(W,F), Y(T,F), Y(F,F) Y(F,W) Y(F,T) (both magazines arrive till Friday)
Y(3) = Y(W,S), Y(T,S), Y(F,S), Y(S,W), Y(S,T), Y(S,F), Y(S,S) (both magazines arrive till Saturday)
To calculate the PMF, we need to calculate the probability for each of the points in Y(0,1,2,3).
Y(0) = Y(W,W)
= 0.26 x 0.26
Y(0) = 0.0676
Y(1) = Y(W,T) + Y(T,T) + Y(T,W)
= (0.26 x 0.39) + (0.39 x 0.39) + (0.39 x 0.26)
= 0.1014 + 0.1521 + 0.1014
Y(1) = 0.3549
Y(2) = Y(W,F) + Y(T,F) + Y(F,F) + Y(F,W) + Y(F,T)
=(0.26 x 0.25) + (0.39 x 0.25) + (0.25 x 0.25) + (0.25 x 0.26) + (0.25 x 0.39)
= 0.065 + 0.0975 + 0.0625 + 0.065 + 0.0975
Y(2) = 0.3875
Y(3) = Y(W,S) + Y(T,S) + Y(F,S) + Y(S,W) + Y(S,T) + Y(S,F) + Y(S,S)
= (0.26 x 0.10) + (0.39 x 0.10) + (0.25 x 0.10) + (0.10 x 0.26) + (0.10 x 0.39) + (0.10 x 0.25) + (0.10 x 0.10)
= 0.026 + 0.039 + 0.025 + 0.026 + 0.039 + 0.025 + 0.010
Y(3) = 0.19
y 0 1 2 3
P(Y=y) 0.0676 0.3549 0.3875 0.19
The PMF plot is attached as a photo here.
