Without a calculator match each graph with a function Note t

Without a calculator, match each graph with a function. Note that, not all there functions appear among the given graphs.

Solution

(a) This graph is a upward parabola with vertex at (-1,-1), Therefore, its equation will be in the form (x+1)^2=k(y+1). Which can be rewritten as y=(1/k)(x+1)^2-1. This equation matches with option J (for k=1), therefore, graph (a) matches with equation J

(b) This graph is a periodic function with its period equal to pi and amplitude is almost 0.5. Since the graph starts at origin, therefore it is a sine graph. Hence, the sine function with period = pi and amplitude = 0.5 is y = 0.5sin(2x). Therefore, graph (b) matches with equation A.

(c) This is again a a periodic function with its period equal to pi and amplitude equal to 2. Since it is passes through origin, therefore it is again a sine graph. Hence, the sine function with period=pi and amplitude=2 is y=2sin(2x). Therefore, graph (c) matches with option D.

(d) This graph is of a shifted logarithmic function. Since the graph is shifted towards right by 1 unit, therefore, the equation of the graph will be y=log(x-1). Therefore, graph (d) matches with option Q.

(e) This is a straight line with positive slope and negative y intercept. The online equation of line with positive slope and negative y intercept amongst the given option is y=2x-4. Therefore, the graph (e) matches with option E.

(f) This graph is of an exponential function flipped twice; once around x axis and once around y axis. Therefore, it\'s equation will be of the form y=-ae^(-bx), where \'a\' and \'b\' are positive. Therefore, amongst the given options, option C seems correct.