Unit 6: Exponential Functions L2 – Tables of Exponential and Linear Functions Investigating Tables of Exponential and Linear Functions Linear: The table of a linear function shows that the x-values change by a amount. The y-values are by a constant amount. Example: x y -2 8 -1 10 12 1 14 The x-values are increasing by and the y-values are being by 2. Remember the equation for a line is y = mx + b. From the table, what is the y-intercept? What is the slope of this line? Therefore, what is the equation of this function?

Exponential: The table of an exponential function shows that as the x-values change by a amount, the y-values are by a constant amount. Example: x y 2 1 6 18 3 54 4 162 The x-values are increasing by and the y-values are being by 3.   Remember, the general equation of an exponential function is f(x) = a(bx). What is the “a” value for the above exponential function? What is the “b” value? (HINT: what are the y-values being multiplied by?) Therefore, what is the equation of this function?

Practice: Determine which type of function (linear or exponential) each table represents. Then write the equation for the function. 1.) 2.) 3.) 4.) x Y -4 3 -2 2 1 4 -1 6 8 -3 x Y -1 1.5 3 1 6 2 12 24 4 48 5 96 x Y -2 16 -1 8 4 1 2 3 .5 .25 x Y -1 2 1 5 8 3 11 4 14 17

Write the equation for each graph. 5.) 6.)