Question

You have learned about quadratic and linear function in earlier grades.  Explain in a variety of ways how you can distinguish the exponential function  from the quadratic function  and linear function . (Hint: compare the rate of change using finite differences in tables of values; identify a constant ratio in the table of values).  

https://i.gyazo.com/28335b11d0f859c660a9c40ff0de71b5.png 

Answer 1

solution: Let's Distinguish the function f(n) = 2x fn) = x² and fo)=22 from x= -5 to x=5 for Let tabulate some data llustration x | fon) = 2* from= x² fm)=2x We see that 32 -4 -4 2 -3 2 (-5)=Y 2x–5)= -10 th 43-16 2x64)= -8 Ś |-3)= 9 2x+3)= -6 t €2)² = 4 2 *(-2) -- (-12 = 1 2x(-) = -2 -3 - 2 22 2 the values of the Function varies di differenty for all the function defined by the rate of Change given by dy 0 0 1 1 2 2 2' - 2 22 4 23 28 24 = 16 4. 9 4 an 3 6 g 10 4 5 B 32 28 10 an Plotting the graph from date 14 km) zx=h (2,4) ave We see the graph of all three function different in their curvature. Hence all the three function are unique

Calcutting Rate of change of function. in interval - tos for fing= 22 f(s) - f(-5) 32- 32 + 1 / 2 rate = 5+5 5-65) Rate of chane 32.03125 10. 3.203125 For fa 2 25- 25 f(s) - f(-5) s-(-5) for fing - 2x 10 -(-10) 20 f(s) - f(-5) 54-5) 20 - 2 10 We see that the rate of change is different of all the three function in interval of x=-5 to 2=5 Also wsing calculus a (2²) = 2%, lua Au the rates are d £u?) = 24 diff event, d (2x) = 2 an