1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
swat32
2 years ago
8

The graph of g(x) is a transformation of the graph of f(x)=3x. Enter the equation for g(x) in the box. G(x) =.

Mathematics
1 answer:
dalvyx [7]2 years ago
8 0

Function transformation involves changing the form of a function

The function g(x) is \mathbf{g(x) = 8(2)^x}

The function is given as:

\mathbf{f(x) = 3^x}

g(x) is an exponential function that passes through points (-2,2) and (-1,4).

An exponential function is represented as:

\mathbf{y = ab^x}

At point (-2,2), we have:

\mathbf{2 = ab^{-2}}

At point (-1,4), we have:

\mathbf{4 = ab^{-1}}

Divide both equations

\mathbf{\frac 42=\frac{ab^{-1}}{ab^{-2}}}

Simplify

\mathbf{2=\frac{b^{-1}}{b^{-2}}}

Apply law of indices

\mathbf{2=b^{-1+2}}

\mathbf{2=b}

Rewrite as:

\mathbf{b =2}

Substitute 2 for b in \mathbf{2 = ab^{-2}}

\mathbf{2 =a(2^{-2})}

This gives

\mathbf{2 =a(\frac 14)}

Multiply both sides by 4

\mathbf{a = 8}

Substitute 8 for (a) and 2 for (b) in \mathbf{y = ab^x}

\mathbf{y = 8(2)^x}

Express as a function

\mathbf{g(x) = 8(2)^x}

Hence, the function g(x) is \mathbf{g(x) = 8(2)^x}

Read more about exponential functions at:

brainly.com/question/11487261

You might be interested in
A card is drawn from a well shuffled deck of 52 cards. Find the probability that the card is a red card or a 2.
tamaranim1 [39]
|\Omega|=52

There are 26 red cards and four 2's. But two 2's are red, so |A|=26+4-2=28

P(A)=\dfrac{28}{52}=\dfrac{7}{13}\approx54\%
3 0
3 years ago
A watch cost $75.99. If the sales tax rate is 6.25%, what is the amount of sales tax?
Luden [163]

75.99*0.0625=4.75 hope helps

7 0
3 years ago
PLS HELP OLL GIVE BRAINLIEST
Rudiy27

Answer:

yes they are the same

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Find the area of the shaded region.
Arisa [49]
The area of the shaded region is the square subtract the circle. The radius of the circle is the diameter/2
Area of circle= pi x radius x radius
=3.14 x 5 x 5 = 78.5
Area of the square = side x side
= 10 x 10 = 100
Area of shaded 100 - 78.5 = 21.5
And don’t forget the unit of measurement (meters)
8 0
3 years ago
Read the following statement: x + 6 = 6 + x. This statement demonstrates:
ololo11 [35]
The reflective property
7 0
3 years ago
Other questions:
  • What are multiples of the factors of 15
    8·2 answers
  • Answer of question to know what to do the answer
    9·1 answer
  • Use a calculator to find the approximate value of sin-1 (0.549)
    14·2 answers
  • K plus 22 for khan academy
    5·1 answer
  • Help me!!!! Pleaseeee
    7·1 answer
  • 2x-21+6=x-3. How would you solve this
    13·1 answer
  • Yoku Is putting on sunscreen. He uses 2 ml to cover 50 cm? of his skin. He wants to know how many milliliters of sunscreen he ne
    5·1 answer
  • Find the 86 term of the arithmetic sequence 18, 21, 24
    15·2 answers
  • A, B & C form the vertices of a triangle, where
    10·1 answer
  • How can I prove this answer
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!