Monday,+February+1,+2010Set+6

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Problem 1: Jonathan a. Vending machine #2 is the bad one, because S is not a function of N. When you push a button, you do not know what snack you are going to get - it could be any one of multiple snacks. This is not the sign of a function, because in a function, you should only get one value for each input.

b. In vending machines #1 and #3, S is a function of N. The means that each button (n-value) will only give you one snack (s-value). This is the sign of a consistent function.

c. In vending machine #3, N is not a function of S. This means that there are multiple buttons (values of N) which give you the same snack (value of S). Because there are multiple values for each input, N is not a function of S.

Problem 2: James table 1 quadratic table 2 linear table 3 linear table 4 neither

3: Jeremy J(-1) = 1/2 J(-2) = 1/4 J (-3) = 1/8 J(5) = 32 The domain of the function is all real numbers. The range of the function is y > 0.

4: Gilad a. 1 b. 3 c. 9 d. 1/3 e. 1/9 g. There is no x intercept for the graph, because the function never touches the x axis. The y intercept is (0, 1). h. The Domain for this function is x=all real numbers i. This function, e(x) = 3ˆx, is similar to J(x) =2ˆx is the same type of curve, except it is steeper. It has the same y intercept as well. j. x=5 k. x=-3 l. e(1/2) = 1.732 or √3 m. x = 1.465 or log(5)/log(3)

5: Cooper a. 1 b. 1/3 c. 1/9 d. 3 e. 9 a. no x-intercept, because the function never touches the x axis. The y-intercept is (0, 1). b. Domain: x is all real numbers Range: y > 0 c. The domain and the range are similar with the graph of e(x)=3^x. Also it is just as steep just in the other direction. d. x = -5 e. x = 3 f. (.5, .577) or (.5, 1/3^.5) g. (1.465, 5) h. e(x) = 1/3^x

6: David There are two main characteristics of an exponential function. The first is that the domain is all real numbers. The other is that the range is y>0.

7. Sam H a. i.1 ii. -2 I believe these are answers to #8; what about the answers to #7? What are some points that satisfy y = 1^x? iii. 4 iv.-8 v.-1/2 vi. -1/4 vii. -1 vii. -1/4

b. x>any number y>1

c. yes they are both similar

d. same thing just sloping down to the right

8. Jack g(0)=1 g(1)= -2 g(2)= 4 g(3)= -8 g(-1)= -1/2 g(-2)= 1/4 g(1/2)= no solution g(-1/2)= no solution

b.)x=all real numbers y= all real numbers except for 0 But it seems as though x cannot be a fraction -- at least not with an even denominator. How can we possibly express "all real numbers except for fractions with even denominators?" c.) No d.) It would look the same as a whole number function, just reversed Yes -- this is called a reflection over the y-axis!

9. Sara H. 1. If a number is inserted into a function, the outcome is one number only. 2. exponential functions start very small and grow bigger, and eventually shoot straight up 3. exponential functions cross the y axis 4. the range for exponential graphs is usually infinite (all positive numbers) 5. if the exponent in the function is positive, the graph is positive numbers in the right upper hand section of a graph 6. if the exponent in the function is negative, the graph is negative numbers and shoots up towards the left section of the graph 7. exponential functions do not have x-intercepts