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jasenka [17]
3 years ago
6

The slope of a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be translated

to the left or right to represent the same function d(x)? Explain your answer.
Mathematics
1 answer:
soldi70 [24.7K]3 years ago
5 0

Answer:

Left 4 units

Step-by-step explanation:

h(x) is a line with slope 2.  Let's say it has y-intercept b.  So:

h(x) = 2x + b

d(x) is h(x) shifted up 8 units.  So:

d(x) = h(x) + 8

d(x) = 2x + b + 8

We want to shift h(x) left or right to get d(x).  If we say that shift is a units to the right, then:

h(x−a) = d(x)

2(x−a) + b = 2x + b + 8

2x − 2a + b = 2x + b + 8

-2a = 8

a = -4

a is negative, so the shift is to the left.

h(x) should be shifted to the left 4 units.

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The third term of an arithmetic sequence is 14 and the 9th term is -1. Find the first four terms of the sequence.​
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Answer:

The first four terms of the sequence are :  19, 16.5 , 14 , 11.5

Step-by-step explanation:

In the given sequence:

a(3) =  14, a(9)  = -1

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a(n) = a + (n-1)d

a(3) = a + (3 -1) d = a + 2 d

and a(9) = a + (9- 1 ) d = a  + 8 d

⇒   a + 2 d =  14      .........  (1)

and a + 8 d  = -1    ...........  (2)

Now, solving the given system of equation, we get:

From (1), a  = 14 - 2 d

Put in (2), we get:

a + 8 d  = -1                ⇒   14 - 2 d + 8d = -1

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or, d  = -2.5

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a = 19

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Hence, the first four terms of the sequence are :  19, 16.5 , 14 , 11.5

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3 years ago
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