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Licemer1 [7]
3 years ago
6

How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^x compare?

Mathematics
2 answers:
Dafna11 [192]3 years ago
7 0

Answer:

Exponential function is of the form: y =ab^x

where a  is the initial value and b is the growth factor.

  • If b> 1, then the function is exponential growth function.
  • If 0<b<1, then the function is exponential decay function.

Given the parent function:

f(x)=y = (\frac{3}{2})^x            ....[1]

This function is an exponential growth function.

The rule of reflection over y-axis:

(x, y) \rightarrow (-x, y)

Apply the rule on f(x) we get;

(\frac{3}{2})^{-x} = (\frac{2}{3})^x =g(x)

Therefore, the function g(x) =(\frac{2}{3})^x is the graph of the function f(x) reflected over y-axis.

Pani-rosa [81]3 years ago
6 0
Sample Response: The graphs are reflections of each other over the y-axis. The graph of g(x) shoes exponential decay, while the graph of f(x) shows exponential growth.
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Darya [45]

Answer:

(a)Charlie is right

(b)$0

Step-by-step explanation:

(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.

In the game, the possible outcomes are: HH, HT, TH and TT.

Charlie wins when the outcome is HH, TT

  • P(Charlie Wins)=2/4
  • P(Charlie Losses)=2/4

Lucy wins when the outcome is HT or TH

  • P(Lucy Wins)=2/4
  • P(Lucy Losses)=2/4

Therefore, the game is fair. Charlie is right.

(b)

If the outcome is HH, Lucy pays $3.

If the outcome is HT or TH, Lucy gets $2.

If the outcome is TT, Lucy pays $1.

The probability distribution of Lucy's profit is given below:

\left|\begin{array}{c|c|c|c}$Profit(x)&-\$3&-\$1&\$2\\P(x)&1/4&1/4&2/4\end{array}\right|

Expected Profit

=(-3 \times \frac14)+(-1\times \frac14)+(2 \times \frac24)\\=$0

Lucy's expected profit from the game is $0.

7 0
3 years ago
Find the missing segment in the image below​
Bogdan [553]

Answer:

3

Step-by-step explanation:

Intercept theorem

DE // CB ⇒ \frac{AD}{AC} = \frac{AE}{AB}

⇒ \frac{6}{6+?} =\frac{4}{4+2}

⇒ ? = 3

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Allisa [31]

Answer:Alex earned $12

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Step-by-step explanation:

j=3a

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Step-by-step explanation:

the rest of the answers are the same and it is harder to compare if the lines are connected because you are most likely going to use a bar graph

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