4.1 Exponential Functions PDF

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24 problems all answers are there. Didn’t go in order...

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Exponential Functions Introduction and Exploration I would advise you to print this page. As you go through the steps on this sheet, open the Exponential Exploration Homework (listed next in this folder) and select your answers to the questions from this sheet. Some Basic Info on Exponential functions. x • An exponential function is a function in the form f(x) = k·a where a and k are constants and x is the variable. Notice that the key is that the exponent is the variable. • In this general form it is also true that a is positive and does not equal 1. Some Exploration Into the Properties of Exponential Functions Using your graphing calculator graph each of the following functions in the standard window. y = 2x. y = 3x y = 4x y = 5x 1. What point do all of the graphs share (give the coordinates)? 2. What happens as you change the value of a (as it goes from 2 to 5)? 3. What is the domain for these four functions (you may use your graph and your common sense for this one)? 4. What is the range for these four functions (again use your calculator and some common sense to help you)? 5. For all four functions as x → −∞, y → x

1 Remove those graphs from your calculator and graph y =   and y = 2 − x . 2 6. What do you notice about these two graphs?. 7. Explain your answer to number 6 using rules of exponents to help you explain (you may also use any other rules that may be relevant) Some rules of exponents are listed on the next page if you need a refresher. 8. How do these relate to the first four graphs you looked at? __. 10. What is the domain for both of these functions?

Quick Reminder on Rules of exponents a n ⋅ a m = a n +m (multiplying with the same base, add the exponents)

( a n ) m = a nm (raising a power to a power, multiply the exponents) an a

m

= a n− m (dividing with like bases, subtract the exponents)

a −n =

1 an

a 0 = 1 (anything to the zero power is one)...