Which of the following functions represents the following graph?

Question

graph begins in the second quadrant and decreases until negative 2, negative 1 and increases into the first quadrant as x increases.

 

Choose one answer. 
A. f(x) = the square root of the sum of x and 2 - 1\
 
B. f(x) = (x + 2)2 - 1  

 

C. f(x) = negative 1 over x plus 2

 

 
D. f(x) = (x + 2)3 - 1

 
 

Answer 1

If by "negative 2, negative 1" you mean (-2, -1), then

(a) this point must be on the curve and

(b) the curve must be 2nd order to have both negative and positive slopes. So:

 

looking at (a):

(A)  f(x) = f(-2) = sqrt ((-2)+ (2-1)) = sqrt(-2 +1) = sqrt (-1) = i <> -1 → (A) is not the answer

 

(B)  f(x) = f(-2) ((-2) + 2)^2 - 1 = (0)^2 - 1 = 0 - 1 = -1 =-1 → (B) could be the answer

 

(C)  f(x) = f(-2) = -1/((-2) + 2) = -1/0 = infinity <> -1 → (C) is not the answer

 

(D)  f(x) = f(-2) = ((-2) + 2)^3 - 1 = 0^3 - 1 = 0 - 1 = -1 = -1 → (D) could be the answer.

 

looking at (b):

 

(B) is second order which means it will change slope once (think a parabola which is second oder → (B) could be the answer

 

(D) is third order, which means it will change slope once → (B) is not the answer.

 

So the answer is (B)