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Algebra 2 Final review part 2

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1) what is the range of    y = 3 sqrt (x+6)

2) find the solution(s) to x+1 = sqrt(2x + 5)

3) for the sequence 2/3 , 2/9 , 2/27 , 2/81 write the nth term formula     (Is it geometric or arithmetic? How do i know?)

4) find an equation for the inverse of the relation y = 9x+5

5) identify zeros and asymptotes of f(x) = (3x^2 + 2x - 8)/ (x^2 - 9)

Jan 31, 2019

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1) what is the range of    y = 3 sqrt (x+6)

I believe this might be  y = ∛ (  x + 6)

As x assumes some large negative value........y tends toward - inf

As x assumes some large positive value......y tends toward inf

So   the range is (-inf, inf)

2) find the solution(s) to x+1 = sqrt(2x + 5)

Square both sides

x^2 + 2x + 1 = 2x + 5       rearrange as

x^2 - 4 = 0         factor

(x + 2) (x - 2)  = 0

Setting each factor to 0 and solving for x we get that  x = -2    or  x = 2

The second solution is good

The first  is extraneous.....it makes the left side of the original equation negative....but we cannot get a negative from a positive radical   Jan 31, 2019
#2
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3) for the sequence 2/3 , 2/9 , 2/27 , 2/81 write the nth term formula     (Is it geometric or arithmetic? How do i know?)

Geometric....the common ratio is  1/3

Arithmetic sequences hve a common difference between terms, not a common ratio between terms

The nth term formula is     (2/3)(1/3)^(n - 1)

4.   y = 9x + 5       subtract 5 from both sides

y - 5 =  9x          divide both sides by  9

[ y - 5  ] / 9 = x            "swap" x and y

[ x - 5 ] / 9 = y          the inverse   is in red   Jan 31, 2019
#3
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5) identify zeros and asymptotes of f(x) = (3x^2 + 2x - 8)/ (x^2 - 9)

The numerator determines the zeroes

3x^2 + 2x - 8 = 0

(3x - 4) (x + 2) = 0

Setting each factor to 0 and solving for x gives the zeroes of x = 4/3  and x = -2

We have same power polynomial / same power polynomial    situation

The horizontal asymptote comes from the ratio of the coefficients on the x^2 terms

This is

y = 3/1   =  3

The vertical asymptotes are the x values that make the denoninator = 0

Note that these are  x = 3      and x = -3   Jan 31, 2019