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
Mkey [24]
3 years ago
14

Write a formula for function f in terms of function g.

Mathematics
1 answer:
emmasim [6.3K]3 years ago
7 0
\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}
\end{array}

\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\
\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\
\end{array}

\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{  D}}\\
\qquad if\ {{  D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{  D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{  B}}}
\end{array}


so hmm if you notice, your f(x) there, looks just like g(x), but is "shifted horizontally" by about 9 units to the right

that simply means, based on that template above, that C/B = -9, and we can simply make B = 1  and C = -9, and we get C/B = -9/1 which is -9

thus   \bf \begin{array}{llcll}
f(x)=g(&1x&-9)\\
&\uparrow &\uparrow \\
&B&C
\end{array}\iff f(x)=g(x-9)
You might be interested in
If a(x) = 3x + 1 and b(x)= √x-4 , what is the domain of (b*a)(x)
kondor19780726 [428]
A(x) = 3x + 1
b(x) = √(x-4)

Therefore
(b \circ a) (x) = \sqrt{3x+1-4} =\sqrt{3x-3}
This composition of functions is only defined as a real number when x≥0.
Therefore its domain is x = [1,∞]

Answer: [1,∞]
5 0
3 years ago
Read 2 more answers
Explain in words how to find the product of -4 (-1.5) using a number line.where do you end up
Ierofanga [76]

Answer:

To multiply two minus numbers they  will result as a positive number.

the product of any numbers when there is a negtive will always have 2 negtives invlved form three numbers including the answer.

-4 x -1.5 is the same as 4 x 1.5

the answer is  6

Three numbers like -1 x  4 will also be 2 numbers of negative.

= -4

We change this to -4 x 1.5 and shows the answer as -6

But the question had 2 negative numbers already and the answer is just positive 6.

8 0
3 years ago
Read 2 more answers
7. Write the equation of the line that is perpendicular to y = -5x + 1 and passes through the point (2,-1). slope intercept equa
Svetach [21]

Answer:

y = 1/5x - 7/5

Step-by-step explanation:

y = 1/5x + b

-1 = 1/5(2) + b

-1 = 2/5 + b

-7/5 = b

4 0
2 years ago
There are 2 squares and 8 circles. What is the simplest ratio of squares to total shapes?​
Veronika [31]

Answer:

1/4

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
If the common difference of an ap is 3/2 and its 20 th term 35×1/2 find first term and 15 th term
Lady bird [3.3K]

Answer:

Step-by-step explanation:

d = 3/2

a₂₀ = a₁+19d

35/2 = a₁ + 19×3/2

a₁ = 35/2 - 19×3/2 = -11

a₁₅ = a₁+14d = -11 + 14×3/2 = 10

4 0
3 years ago
Other questions:
  • Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of tr
    12·1 answer
  • How do you multiply
    10·2 answers
  • Can someone please help me
    11·1 answer
  • What is the equation of y = x3 with the given transformations? horizontal translation right 10 units and vertical translation do
    10·2 answers
  • Which expression models the following<br> phrase: "an hourly wage of $12.75"?
    10·1 answer
  • HELP! WILL GIVE BRANLIEST!
    10·1 answer
  • Which tree diagram shows all the possible outcomes for 2 coin flips?
    10·1 answer
  • 5 and 6 why they keep giving me this lol
    6·1 answer
  • Classify the following triangle. Check all that apply .
    11·2 answers
  • PLZ HELP MEH FOR A BUNCH O POINTS PLLLLLLZZZZZZZZZ I NEED NUMBER 2 BASED ON NUMBER 1!!!!!!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!