Bellringer 52 = 25 = 72 = 49 = 92 = 81 = Looking at the three examples above, do you notice a relationships between the square roots and the exponents. Write at least one observation you have in your bellringer.

Square roots, Exponents, and Exponential Functions Algebra I Kenwood Academic Center March 2014 Square roots, Exponents, and Exponential Functions

Relationship Between Roots and Exponents Another way to write a radical expression is to use a rational exponent. Like the radical form, the exponent form always indicates the principal root. √25 = 25½ 49 = 491/2

Example One (16y2) ½ Solution: 4y

Examples 2 (64x16)-1/2 Solution: 1/8x8

Your Turn! (49x24 y12)-1/2 Solution: 1/7x12 y6

What we know: 1. How to graph Lines 2 What we know: 1. How to graph Lines 2. What a function is (vertical line test) Graph the line: Y=-4x+3 What is the slope? What is the y-intercept? Is this a function?

We’ve looked at linear functions We’ve looked at linear functions. We are now going to study a new function called exponential functions. They are different than any of the other types of functions we’ve studied because the independent variable is in the exponent. Let’s look at the graph of this function by plotting some points. x 2x 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 3 8 2 4 BASE 1 2 0 1 Recall what a negative exponent means: -1 1/2 -2 1/4 -3 1/8

Friday Riddle Ron Weasley once again has not done his assignment for his Defense Against the Dark Arts Course and asks Hermione to help him. She is, once again, very frustrated with Ron, but as we know, She is in love with him so she strikes a deal with Ron. Hermione tells him that she will help him with half the assignment each day throughout the week. Ron, being the slightly lazy student that he is agrees and each day throughout the week Hermione helps him but he does no work outside of her help. Will he finish the assignment with Hermione’s help? Why or why not?

Compare the graphs 2x, 3x , and 4x Characteristics about the Graph of an Exponential Function where a > 1 1. Domain is all real numbers 2. Range is positive real numbers 3. There are no x intercepts because there is no x value that you can put in the function to make it = 0 What is the range of an exponential function? What is the x intercept of these exponential functions? What is the domain of an exponential function? Are these exponential functions increasing or decreasing? What is the y intercept of these exponential functions? 4. The y intercept is always (0,1) because a 0 = 1 5. The graph is always increasing

If au = av, then u = v This says that if we have exponential functions in equations and we can write both sides of the equation using the same base, we know the exponents are equal. The left hand side is 2 to the something. Can we re-write the right hand side as 2 to the something? Now we use the property above. The bases are both 2 so the exponents must be equal. We did not cancel the 2’s, We just used the property and equated the exponents. You could solve this for x now. Let’s do a few examples

Homework!!!