Monday,+February+1,+2010+Set+3

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Please enter your answers here. Use full sentences. Don't use the word "it" without making sure that the reader knows to what you are referring.

Problem 1: Maya a) Vending machine #2 is bad to use because for each button (N), there are two options for S, so it is not a function.

b) For vending machines 1 and 3, S is a function of N. It makes them user friendly because you know what you're going to get when you press a button.

c) N is not a function of S for machine 3. This means that there are multiple values for N with one value for S.

Problem 2: Elena Table 1: quadratic Table 2: linear Table 3: linear Table 4: neither

3: Jacob ???

4: Tyler a. 1 b. 3 c. 9 d. 9 e. 1/3 f. 1/9

I do not know how to get the graph up here, but just imagine Sarah's except flipped left to right.

g. no x intercept. y intercept = 1 h. domain = all real numbers, range = x>0 i. It has the same general shape, range, domain, and y intercept. j. 5 k. -3 l. √3 or 1.732 m. 1.456

5: Sarah a. 1 b. 1/3 c. 1/9 d. 3 e. 9



a. there are no x-intercepts. the y-intercept is 1 b. domain= all real numbers range= y>0 c. the graph of e(x)= 3^x and my graph both have a y-intercept of 1 and no x-intercepts d. -5 e. 3 f. (1/2, 1/√3) and (1/2, -1/√3) or (0.5, 0.577) and (0.5, -0.577) g. when e(x)=5, x≈ -1.456 h. e(x)= 1/3^x

6: Max What general characteristics do exponential functions have? The domain is all real numbers and the range is y>1 If the base is 1 then y=1. The y intercept would be 1 and there would be no x intercept. The shape of the graph is a parabola.

7. Josh Question: What would happen if we let the base be equal to 1? Find points and sketch the graph of f(x)=1^x. Does this share the characteristics listed in problem #6?.

A. If we let the base be equal to 1, the y value will always be equal to one. No matter what you do, 1 to any exponent will always equal 1. So on a graph the y value will always be equal to 1 for every x value. B. Graph: C. This type of equation does share characteristics that lie in problem number 6. For example, some characteristic for an exponential function are, they cross the y-axis, the domain is always all real numbers, and never touches the x-axis. For this problem, all these characteristics are true. This graph follows all of those characteristics listed.

8. Dan

The range could be negative. a. i. 1 ii. -2 iii. 4 iv. -8 iv. (again) -1/2 v. 1/4 vi. Does not exist vii. Does not exist b. The domain of the function is all real numbers. The range is not all real numbers, because when taking an even root of a negative number, the number returned is imaginary, or does not exist. The domain of the function would contain infinitely many numbers. Hmmm...so even if the domain contains infinitely many numbers, would it be "all real numbers?" would 1/2 be in the domain? 1/4? 1/6? 1/8? In fact, could you have any fraction with a denominator that was an even number? What would the domain look like if you took all real numbers, with the exception of these fractions??? Cohesive, complete, or not? c. The similar characteristic is that the domain contains infinitely many numbers. Otherwise, it has different properties. d. An exponential equation with a fraction as the base would have a graph similar to an exponential equation with a negative exponent. In other words, it would have a range greater than 0 and an infinitely many numbers in the domain.

9. Drew After completing this packet i realized that i learned a lot. I learned how to determine what is a function and what is not a function. I also learned how to determine weather a table is quadratic or linear. Also I learned how to determine the range and domain. And finally I learned that a Y can have 2 X values on a graph. Overall i feel like a learned a good amount from this math packet.