MATH 107 homework

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MATH 107 Name: ________________________________

Directions: Fill out this answer sheet. Either select the correct answer or fill in the blank. Failure to use this answer sheet will result in an automatic 5 pt deduction. Create a single pdf file with this answer sheet first and any work you want me to consider for partial credit.

Section 1.6

1. Sketch the graph of the given function, identify any intercepts, and test for symmetry. You must show work for credit.

x-intercept(s):_______________

y-intercept(s):_______________

Symmetry about x axis? Yes No

Symmetry about y axis? Yes No

2. Determine analytically if the following function is even, odd, or neither.

3. The function to the right is a polynomial. Just by examining the graph answer the following questions:

Is this graph of an even function?

Yes or no

Draw a square on the absolute minimum for this function.

Draw a triangle on the relative maximum for this function.

Draw a circle on the relative minimum.

Draw a cross on the inflection points of this graph.

The degree of the polynomial (highest exponential power) is what?

a. 3

b. 4

c. 5

Section 1.7

4. Suppose (1, -3) is on the graph of y = f(x). Use Theorem 1.7 to find the point on the graph of the given transformed function.

5. Let . Find a formula for a function g whose graph is obtained from f from the point sequence of transformations.

(1) Shift left 4 units; (2) shift down 3 units.

Section 2.1

Find both the point slope and slope-intercept form of the line with the given slope and passes through the given point.

point-slope: _________________________,

slope-intercept form: ________________________

7. The temperature T in degrees Fahrenheit t hours after 6 AM is given by:

a. Find T(4) = _________; T(9) = ______________; T (12) = ____________

b. Find and interpret the average rate of change of T over the interval [5,9].

DT/Dt = ____________ degrees/hour

Section 2.2

Graph the function. Find the zeros of each function and the x- and y-intercepts of each graph if any exist. From the graph, determine the domain and range of each function, list the intervals on which the function is increasing, decreasing or constant, and find the relative and absolute extrema, if they exist.

Section 2.5

9. According to this website, find the census data for Lorain County, Ohio is.

Year	1970	1980	1990	2000
Population	256848	274909	271126	284664

(a) Find the least squares regression line for these data and comment on the goodness of fit. Interpret the slope of the line of best fit.

(b) Use the regression line to predict the population of Lorain County in 2020.

10. Please answer the following questions:

1. A fourth-grade class decides to enclose a rectangular garden, using the side of the school as one side of the rectangle. What is the maximum area that the class can enclose with 64 ft of fence? What should the dimensions be in order to yield this area?

2. For the problem above, suppose the following:

The length of fence is L (a constant).

One side of the fence is x (the variable).

For what values of x is the Area enclosed equal to zero?

For what value of x is the area a maximum?