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3 years ago

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The exponential function, f(x)=2^x, undergoes two transformations to g(x)=3x2^x+5. How does the graph change? Select all that ap

ply (choose two)

1 answer:

Shalnov [3]3 years ago

5 0

Answer: Options A and C.

Step-by-step explanation:

The parent exponential function has the form:

$f(x)=b^x$

This can be transformated as following:

When you multiply the function by a factor <em>a</em> ( $a*f(x)$ )<em> </em>and <em>a>0 </em>, then the function is vertically stretched.

When you add a number <em>k</em> to the parent function, the function is shifted up ( $f(x)+k$ )

The parent function given in the problem is:

$f(x)=2^x$

To obtain the function $g(x)=3*2^x+5$ , the parent function is multiplied by a factor 3 (which is greater than 0) and the number 5 is added.

Therefore, the graph is shifted up and vertically stretched.

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A fish tank has 35 gallons of water in it, but suddenly starts leaking. Water is leaking from the tank at a rate of 1/4 gallon p

Norma-Jean [14]

Answer:

35 - m

Step-by-step explanation:

A tank containing 35 gallons of water is leaking at a rate of gallon per minute.

"m" represents the number of minutes spent

Number of gallons left in the tank = initial amount of water present – leaked amount of water

Number of gallons of water left = 35 gallons – number of minutes spent rate of leakage.

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3 years ago

What is 6pi to the 6 power.

Tomtit [17]

Hey there!

6(3.14)^6

= 6(3.14^6)

= 6(3.14 * 3.14 * 3.14 * 3.14 * 3.14 * 3.14)

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= 6(97.21171216 * 9.8596)

= 6(5,750.811583)

≈ 5750.81158328

Therefore, the answer should be:

5,750.81158328

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

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2 years ago

Willl give 100 points!! <br> Find the exact value of sine, cosine and tangent.

mezya [45]

Answer:

Step-by-step explanation:

c i think

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3 years ago

PLZ HELP!!! I don't understand.

lilavasa [31]

Answer:

Step-by-step explanation:

14.)

lets first find x:

2x+x+90=189

3x=90

x=30

lets find y:

2y=x

2y=30

y=15

lets find z:

2y+z=180

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6 0

2 years ago

Read 2 more answers

Determine the above sequence converges or diverges. If the sequence converges determine its limit

marshall27 [118]

Answer:

This series is convergent. The partial sums of this series converge to $\displaystyle \frac{2}{3}$ .

Step-by-step explanation:

The $n$ th partial sum of a series is the sum of its first $n\!\!$ terms. In symbols, if $a_n$ denote the $n\!$ th term of the original series, the $\! n$ th partial sum of this series would be:

$\begin{aligned} S_n &= \sum\limits_{k = 1}^{n} a_k \\ &= a_1 + a_2 + \cdots + a_{k}\end{aligned}$ .

A series is convergent if the limit of its partial sums, $\displaystyle \lim\limits_{n \to \infty} S_{n}$ , exists (should be a finite number.)

In this question, the $n$ th term of this original series is:

$\displaystyle a_{n} = \frac{{(-1)}^{n+1}}{{2}^{n}}$ .

The first thing to notice is the ${(-1)}^{n+1}$ in the expression for the $n$ th term of this series. Because of this expression, signs of consecutive terms of this series would alternate between positive and negative. This series is considered an alternating series.

One useful property of alternating series is that it would be relatively easy to find out if the series is convergent (in other words, whether $\displaystyle \lim\limits_{n \to \infty} S_{n}$ exists.)

If $\lbrace a_n \rbrace$ is an alternating series (signs of consecutive terms alternate,) it would be convergent (that is: the partial sum limit $\displaystyle \lim\limits_{n \to \infty} S_{n}$ exists) as long as $\lim\limits_{n \to \infty} |a_{n}| = 0$ .

For the alternating series in this question, indeed:

$\begin{aligned}\lim\limits_{n \to \infty} |a_n| &= \lim\limits_{n \to \infty} \left|\frac{{(-1)}^{n+1}}{{2}^{n}}\right| = \lim\limits_{n \to \infty} {\left(\frac{1}{2}\right)}^{n} =0\end{aligned}$ .

Therefore, this series is indeed convergent. However, this conclusion doesn't give the exact value of $\displaystyle \lim\limits_{n \to \infty} S_{n}$ . The exact value of that limit needs to be found in other ways.

Notice that $\lbrace a_n \rbrace$ is a geometric series with the first term is $a_0 = (-1)$ while the common ratio is $r = (- 1/ 2)$ . Apply the formula for the sum of geometric series to find an expression for $S_n$ :

$\begin{aligned}S_n &= \frac{a_0 \cdot \left(1 - r^{n}\right)}{1 - r} \\ &= \frac{\displaystyle (-1) \cdot \left(1 - {(-1 / 2)}^{n}\right)}{1 - (-1/2)} \\ &= \frac{-1 + {(-1 / 2)}^{n}}{3/2} = -\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\end{aligned}$ .

Evaluate the limit $\displaystyle \lim\limits_{n \to \infty} S_{n}$ :

$\begin{aligned} \lim\limits_{n \to \infty} S_{n} &= \lim\limits_{n \to \infty} \left(-\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\right) \\ &= -\frac{2}{3} + \frac{2}{3} \cdot \underbrace{\lim\limits_{n \to \infty} \left[{\left(-\frac{1}{2}\right)}^{n} \right] }_{0}= -\frac{2}{3}\end{aligned}}_$ .

Therefore, the partial sum of this series converges to $\displaystyle \left(- \frac{2}{3}\right)$ .

8 0

3 years ago