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)

BLANK Jan 31, 2019

#1**+2 **

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

CPhill Jan 31, 2019

#2**+2 **

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

CPhill Jan 31, 2019

#3**+2 **

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

CPhill Jan 31, 2019