+234 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)
+128408 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
+128408 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
+128408 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
