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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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A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance
nataly862011 [7]

The Required ratio between the speed of the boat and speed of the water current is 8:3.

<h3>What is ratio?</h3>

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six.

Given:

Upstream time= 8 hr 48 = 8 4/5 hour

Downstream time= 4 hour

Let the man's rate upstream be x kmph and that downstream be y kmph.

Then,

distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

x* 8 hr 48 min = y* 4 hours

x* 8 4/5= 4y

y= 11/5 x

Now,

Required ratio

(y+x)/2:(y-x)/2

= (16x/5 * 1/2): ( 6x/5 *1/2)

=8/5:3/5

=8:3

Hence, the required ratio is 8:3.

Learn more about ratio here:

brainly.com/question/13419413

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3 0
1 year ago
Mrs. Cho has 24 students in her class. Some of her students are also in the play. Explain why it is not possible for exactly 24%
lora16 [44]
Let's start by calculating how many students does 24% represent.
24% * 24 = 0.24 * 24 = 5.76
We got a decimal number as solution. The reason why exactly 24% students can't be in the play is because this percentage does not represent whole number of students. She can't take 0.76 students

If she wanted 25% students to be in a play it would mean she has to take:
25% * 24 = 0.25 *24 = 6 students
3 0
3 years ago
Please help me need ASAP
Jet001 [13]

(3) y= 5x+ 13

you have to do the rise (ryse - with a y because it is the y value) over the run to get your slope and then subtract your slope from 18 to get 13.

4 0
2 years ago
Is the square of a complex number always a real number? Explain how, please I would like to finish this tonight.
Artemon [7]

Answer:

<em>The absolute square of a complex number is calculated by multiplying it by its complex conjugate. This give the magnitude squared of the complex number. The absolute square is </em><em>A</em><em>l</em><em>w</em><em>a</em><em>y</em><em>s</em><em> </em><em>R</em><em>e</em><em>a</em><em>l</em><em>. We will use complex exponentials all the time.</em>

7 0
2 years ago
Read 2 more answers
What is 5.76 divided by 3.20
Mandarinka [93]

Answer is 1.8

Hope it helps yah

4 0
3 years ago
Read 2 more answers
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