precalc review/calc
posted by jane .
For the curve y=2^[sqrt(9x2)], find the range of the function.
I think the range is [0,8] but I don't know why. Could you show me how to get to that answer? Thanks.

precalc review/calc 
Damon
I assume you mean:
y=2^[sqrt(9x^2)]
we do not want to take the sqrt of a negative number so domain is x<3
or
3 < x < +3
eg
if x = 3 or + 3, y = 2^0 = 1
if x = 1 or + 1, y = 2^sqrt 8 = 7.1
if x = 2 or + 2, y = 2^sqrt 5 = 4.7
if x = 0 , y = 2^3 = 8
So
I think the range of y is 1 to 8, not 0 to 8
that corresponds to y between 0 and 8 so I agree with you 
do NOT agree with you 
Damon
Last sentence is a typo.

precalc review/calc 
jane
Thanks! So because the smallest and biggest numbers +/ 3 and the middle number 0 result in the smallest and largest y values, 1 and 8 respectively, the range is therefore [1, 8]. That makes sense. :D
Respond to this Question
Similar Questions

calculus
Find an expression for the function whose graph is the given curve. a) The bottom half of the parabola x+(y1)^2=0 b) The top half of the circle (x1)^2 + y^2= 0 I think I have a vague idea of what I need to have in my expression for … 
calcius
Determine whether the relation represents a function. If it is a function, state the domain and range. {(2, 1), (1, 2), (0, 3), (1, 2), (3, 6)} a. function domain: {2, 1, 0, 1, 3} range: {1, 2, 3, 6} b. function domain: {1, … 
math
questions involving domain and range... 1. Find the domain of the function f(x)=(3x+1)/(sqrt of (x^2+x2)) andd. 2. Let f(x)= (absvalue(x))/x. Show that f(x)={ 1, x > 0 {1, x < 0 Find the domain and range of f(x). 
AlgebraPlease check
1. solve sqrt (11x) = sqrt(x7) choices are 6,7,8 or9 I think according to my calcs the answer is (9) The range of f(x) = sqrt(3x6)  2 answers would be y<= (2) y>= (2) y> (2) y<=(2) I think the answer is y <= 2, … 
precalc
find the domain and range of the following as an inequality and interval notation. y=sqrtx3 2: y=3x+5 3: y= 2/x7 4; y=2+sqrt x 
Algebra
I think this is a easy trick question, so I probably know the answer but I just wanted to double check. What is the domain and range of the function f(x) = 3^x Find the f^1 and its domain and range? 
precalculus check immediately
suppoe f is a function with domain [1,3]and range[2,5]? 
Pure Mathematics
1. Given that the straight line y=c3x does not intersect the curve xy=3, find the range of values for c. 2. Find the range of values for c for which the line y=cx+6 does not meet the curve 2x^2xy=3. 3. Find the range of values for … 
Calculus
Find the sum and difference functions f + g and f – g for the functions given. f(x) = 2x + 6 and g(x) = 2x  6 f(x) = x^2  x and g(x) = 3x + 1 f(x) = 3x^3  4 and g(x) = x^2 + 3 State the domain and range for the sum and difference … 
Finding Range  Maths
Let f:{x: IxI > 100} => R, f(x) = 1/x^2. State the range of f. Let f:{x: IxI < 0.1} => R, f(x) = 1/x^2. State the range of f. *R = real numbers How do you find the two ranges?