Which of the following functions represents the following graph?

Question

Which of the following functions represents the following graph?


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

Your solution is

 

B)  (x + 2)² - 1

 

 

The function (x + 2)² acts like the graph x².   x² always starts on the second quadrant and decreases in y-value from its starting point as x increases.  If you plug in x = -2, f(-2) = -1.

 

f(-2) = (-2 + 2)² - 1

f(-2) = 0 - 1

f(-2) = -1

 

(-2, 1) is point where the graph starts to increase as the x-values increase.  Also, this point is in the second quadrant.  In addition, the function x² is a reflection over the positive y-axis which is between the first and second quadrants.