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konstantin123 [22]
2 years ago
13

F(x)=4^x and g(x)=4^x+2

Mathematics
1 answer:
dsp732 years ago
3 0

Given:

The two functions are:

f(x)=4^x

g(x)=4^x+2

To find:

The type of transformation from f(x) to g(x) in the problem above and including its distance moved.

Solution:

The transformation is defined as

g(x)=f(x+a)+b                .... (i)

Where, a is horizontal shift and b is vertical shift.  

  • If a>0, then the graph shifts a units left.
  • If a<0, then the graph shifts a units right.
  • If b>0, then the graph shifts b units up.
  • If b<0, then the graph shifts b units down.

We have,

f(x)=4^x

g(x)=4^x+2

The function g(x) can be written as

g(x)=f(x)+2            ...(ii)

On comparing (i) and (ii), we get

a=0,b=2

Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).

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Answer:

Step-by-step explanation:

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Given a term and the common difference, find the explicit formula.<br> 8. a(19) = 135<br> d = 15
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<u>Solution:</u>

Given, a term a(19) = 135 and common difference d = 15

We have to find the explicit formula.

Now, we know that, a(n) = a + (n – 1)d where a(n) is nth term, a is first term, d is common difference,

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\begin{array}{l}{\rightarrow a(19)=a+(19-1) 15} \\\\ {\rightarrow 135=a+18 \times 15} \\\\ {\rightarrow a=135-270} \\\\ {\rightarrow a=-135}\end{array}

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Hence, the explicit formula is a(n) = 15(n – 10).

7 0
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