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Juliette [100K]
3 years ago
9

F(x) = x ^ 2 . What is g(x) ?

Mathematics
1 answer:
Bond [772]3 years ago
6 0

Given:

The function is:

f(x)=x^2

The graphs of functions f(x) and g(x).

To find:

The function g(x).

Solution:

We have,

f(x)=x^2

The function f(x) is vertically compresses to get the graph of the function g(x). So, the function g(x) is:

g(x)=kf(x)

g(x)=kx^2               ...(i)

From the given graph it is clear that the graph of the function g(x) passes through the point (3,3). So, putting x=3 and g(x)=3 in the above function, we get

3=k(3)^2

3=9k

\dfrac{3}{9}=k

\dfrac{1}{3}=k

Putting k=\dfrac{1}{3} in (i), we get

g(x)=\dfrac{1}{3}x^2

Therefore, the correct option is D.

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Help me with this 1,2,3. For each sequence, Determine with whether it appears to be arithmetic If it does find a common differen
pshichka [43]

Problem 1

<h3>Answer: Arithmetic, common difference = -4</h3>

-------------------

Explanation:

Pick any term of the sequence, and subtract off the previous term to find that,

  • term2 - term1 = -12 - (-8) = -12 + 8 = -4
  • term3 - term2 = -16 - (-12) = -16 + 12 = -4
  • term4 - term3 = -20 - (-16) = -20 + 16 = -4

Each time we get the same result, so that means we have an arithmetic sequence with common difference -4

This indicates that adding -4 to each term, or subtracting 4 from each term, will generate the next one.

Eg: term2 = term1 - 4 = -8-4 = -12.

==========================================================

Problem 2

<h3>Answer: Arithmetic, common difference = 5</h3>

-------------------

Explanation:

Similar to problem 1, this sequence is also arithmetic because we add on 5 to each term to get the next one

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  • -1+5 = 4
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Or you could subtract adjacent terms as done in problem 1, to find that the common difference is 5.

==========================================================

Problem 3

<h3>Answer: Not arithmetic</h3>

-------------------

Explanation:

Unlike the previous two problems, this sequence is not arithmetic.

We can see that

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The gaps of 9 and 36 aren't the same. We need the same common difference between any adjacent terms to have an arithmetic sequence.

This sequence is instead geometric because

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  • term4/term3 = 192/48 = 4

Each quotient is 4, showing the common ratio is 4. To find the next term, we multiply the current term by 4. So the next term after 192 would be 4*192 = 768, then 4*768 = 3072 is next, and so on.

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Answer:

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Step-by-step explanation:

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