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Lana71 [14]
3 years ago
15

Graphing exponential functions and then State the domain, range and asymptote​

Mathematics
1 answer:
Luda [366]3 years ago
6 0

9514 1404 393

Answer:

  D: all real numbers

  R: f(x) > 0

  A: f(x) = 0

  (-∞, 0), (+∞, +∞)

  vertical stretch by a factor of 2; left shift 2 units

Step-by-step explanation:

The transformation ...

  g(x) = a·f(b(x -c)) +d

does the following:

  • vertical stretch by a factor of 'a'
  • horizontal compression by a factor of 'b'
  • translation right by 'c' units
  • translation up by 'd' units

For many functions, horizontal coordinate changes are indistinguishable from vertical coordinate changes. Exponential functions tend to be one of those.

__

Using the above notation, you seem to have f(x) = 3^x, and g(x) = 2f(x+2). The transformation is a vertical stretch by a factor of 2, and a translation left 2 units.

__

As with all exponential functions, ...

  • the domain is "all real numbers"
  • the range is all numbers above the asymptote: f(x) > 0
  • the horizontal asymptote is f(x) = 0

The function is a growth function, so ...

  • x → -∞, f(x) → 0
  • x → ∞, f(x) → ∞

_____

<em>Additional comment</em>

The left shift is equivalent to an additional vertical stretch. The function could be rewritten as ...

  f(x) = 18(3^x)

with no left shift and a vertical stretch by a factor of 18 instead of 2.

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2) Abby made 5 1/2 cups of banana pudding. She served 7/8 cup of the pudding to her kids for dessert.
frez [133]

Answer:

<u>37/8</u>

Step-by-step explanation:

we are going to create 5 1/2 into an improper fraction for now, so it is easier to manipulate.

5 1/2 = 11/10

in order to find the answer, we need to set them both to a common denominator(we need to make sure they have the same denominator so it is easier to subtract)

11/2 if we just take 1 of the cups that Abby made and subtract that by 7/8 that give us the answer

11/2 - 1 = 9/2

we will now us the cup we subtracted from that and "give it to the kids"

 1 = 8/8

so

8/8 - 7/8 = 1/8

so we have 1/8 leftover from that cup, so we can add that back

since 1/8 is a hard number to just add off the top of your head, we can just change the denominator of 9/2 into 8 instead of 2:

9/2 = 36/8

so

1/8 + 36/8 = 37/8

so since 37/8 cannot be simplified anymore, the answer is

<u>37/8</u>

3 0
2 years ago
Point P is on line segment OQ. Given OP = 6, OQ = 4x – 3, and PQ = 3x,
Eva8 [605]

Answer:

Hey there!

6+3x=4x-3

6=x-3

x=9

OQ=4x-3

OQ=4(9)-3

OQ=36-3

OQ=33

Let me know if this helps :)

3 0
3 years ago
Read 2 more answers
A real estate agent sells a house for $92,000. She receives a 6% commission on the sale of the house.
denis23 [38]
Okay so just do this equation below.


92,000 x 0.06

And you have your answer!

Answer is 5,520.

Leave a 5 star rating, a thanks, and a most brainy answer!
5 0
3 years ago
Read 2 more answers
Can someone help me plzz??
ki77a [65]

Answer:

(0,20)

Step-by-step explanation:

1) we can represent the situation as coordinates

lets have # of texts be "x" variable

lets have bill be "y" as the y variable is always the dependant variable and the cost of the phone bill is dependant upon the number of texts so

y=mx+b-slope-intercept form

coordinates: (50,25) and (100,30)

slope: (30-25)/(100-50)

5/50=1/10

hence slope=1/10

y=1/10x+b

substitute in a coordinate pair into this equation

25=50*1/10+b

25=5+b

b=20

hence y intercept is (0,20)

8 0
2 years ago
Calculate the capacity in liters of a tin 20m by 15m by 10m.​
rusak2 [61]
20 * 15 * 10 *10^-6
= 0.003
5 0
3 years ago
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