Which function will have a y-intercept at -1 and an amplitude of 2?

Mathematics

2 answers:

Anna35 [415]3 years ago

6 0

The first and 3rd choices are just sin and cos waves, with amplitude of 1 .
So it has to be the 2nd or 4th choice.

The y-intercept is the point on the graph where x=0.
So if the y-intercept is -1, that just means that f(0)=-1 .
So let's test the two choices:

   f(x) = -2 sin(x) - 1

   f(0) = -2 sin(0) - 1
sin(0) = 0 so
   f(0) = -2 (0) - 1 .
That looks like it works.
Just to be sure, let's check the other possible choice.

f(x) = -2 cos(x) - 1

   f(0) = -2 cos(0) - 1

cos(0) = 1 so f(0) = -2 (1)    - 1 = -3 .

Beautiful ! The y-intercept of choice-2 is -1,
and the y-intercept of choice-4 is -3. The answer is choice-2.

baherus [9]3 years ago

5 0

Answer:

the answer is b

Step-by-step explanation:

Im just typing this so it knows that I properly explained

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see the attached figure with the letters

1) find m(x) in the interval A,B
A (0,100) B(50,40) -------------- > p=(y2-y1(/(x2-x1)=(40-100)/(50-0)=-6/5
m=px+b---------- > 100=(-6/5)*0 +b------------- > b=100
mAB=(-6/5)x+100

2) find m(x) in the interval B,C
B(50,40) C(100,100) -------------- > p=(y2-y1(/(x2-x1)=(100-40)/(100-50)=6/5
m=px+b---------- > 40=(6/5)*50 +b------------- > b=-20
mBC=(6/5)x-20

3) find n(x) in the interval A,B
A (0,0) B(50,60) -------------- > p=(y2-y1(/(x2-x1)=(60)/(50)=6/5
n=px+b---------- > 0=(6/5)*0 +b------------- > b=0
nAB=(6/5)x

4) find n(x) in the interval B,C
B(50,60) C(100,90) -------------- > p=(y2-y1(/(x2-x1)=(90-60)/(100-50)=3/5
n=px+b---------- > 60=(3/5)*50 +b------------- > b=30
nBC=(3/5)x+30

5) find h(x) = n(m(x)) in the interval A,B
mAB=(-6/5)x+100
nAB=(6/5)x
then
n(m(x))=(6/5)*[(-6/5)x+100]=(-36/25)x+120
h(x)=(-36/25)x+120
find h'(x)
h'(x)=-36/25=-1.44

6) find h(x) = n(m(x)) in the interval B,C
mBC=(6/5)x-20
nBC=(3/5)x+30
then
n(m(x))=(3/5)*[(6/5)x-20]+30 =(18/25)x-12+30=(18/25)x+18
h(x)=(18/25)x+18
find h'(x)
h'(x)=18/25=0.72

for the interval (A,B) h'(x)=-1.44
for the interval (B,C) h'(x)= 0.72

 h'(x) = 1.44 ------------ > not exist

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