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3 years ago

5

Help lol the question is on the picture please help!

1 answer:

valina [46]3 years ago

7 0

here u go, remember the ratio

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given f(x)=3^x-2 and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur b

Leviafan [203]

Answer:

$g(x)=3^{3x}+2$

The transformation that occurs from $f(x)\rightarrow g(x)$ is compression by 3 units horizontally and shift of 4 units upwards.

Step-by-step explanation:

Given

$f(x)=3^x-2$

$g(x)=f(3x)+4$

Translation Rules:

$f(x)\rightarrow f(cx)$

If $c>1$ the function is compressed $c$ units horizontally.

If $c$ and $c>0$ the function stretches $c$ units horizontally.

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

Applying the rules to $f(x)$

Step 1

$f(x)\rightarrow f(3x)$

$f(3x)=3^{3x}-2$

[compressed $3$ units horizontally]

Step 2

$f(3x)\rightarrow f(3x)+4=g(x)$

$f(3x)+4=3^{3x}-2+4$

∴ $g(x)=3^{3x}+2$

[shifts 4 nits up]

∴ The transformation that occurs from $f(x)\rightarrow g(x)$ is compression by 3 units horizontally and shift of 4 units upwards.

5 0

3 years ago

A, B, and C are collinear, and B is between A and C. The ratio of AB to BC is 3 : 1.

S_A_V [24]

Coordinates of point C: (1,-1)

Step-by-step explanation:

In this problem, A, B and C are collinear, and B is between A and C.

The ratio AB : BC is 3 : 1.

This means that we can write the following two equations:

$x_B-x_A = 3(x_C-x_B)\\y_B-y_A=3(y_X-y_B)$

where:

$(x_A,y_A)=(-7,3)$ are the coordinates of point A

$(x_B,y_B)=(-1,0)$ are the coordinates of point B

$(x_C,y_C)$ are the coordinates of point C

Solving the equation for $x_C$ ,

$x_C = x_B + \frac{x_B-x_A}{3}=-1+\frac{-1-(-7)}{3}=1$

Solving the equation for $y_C$ ,

$y_C=y_B + \frac{y_B-y_A}{3}=0+\frac{0-3}{3}=-1$

So, the coordinates of point C are

$C(-1,1)$

Learn more about how to divide segments:

brainly.com/question/3269852

brainly.com/question/11280112

#LearnwithBrainly

4 0

3 years ago

Give an exponential formula for the number of hiv infections, upper h, (in millions) as a function of years, t, since 1985. Use

ollegr [7]

we can sue formula

$P(t)=P_0e^{kt}$

where

P(t) is population after t years

P0 is initial population

k is growth rate

t is time in years since 1985

Let's assume

h(t)=P(t) is million

h_0=P_0 in million

we can replace it

and we get

$h(t)=h_0e^{kt}$ ..............Answer

7 0

3 years ago

I have 10 questions can someone help me please 1 9/5+8/5. 2 1/3+1/3 3 2/4+1/4

Papessa [141]

Answer:

1. 3 2 /5

2. 2/ 3

3. 3/4

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

How do I find the indicated value?

spin [16.1K]

Step-by-step explanation:

using this

t_n = a+ (n-1)d

5 0

3 years ago