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Graphs and Functions

Maximum Value of a Function

Suppose that a projectile is fired at an angle of 45 degrees from the horizontal.... Please see attachment and show work.

Characteristic Function of Metric Space

Let S ⊂ M. (a) Define the characteristic function Xs : M --> R. (b) If M is a metric space, show that Xs(x) is discontinuous at x if and only if x is a boundary point of S. [Please see attached PDF file for full problem]. for part (a), I think something similar to http://planetmath.org/encyclopedia/Characteristi

Lines Parallel To y=-x+6

Find an equation of the line that is parallel to the line y = -x + 6 and that passes through the point (5,9).

Basic 25

Graph function and state domain and range 2 y=x -2x+1

Slope

Here I go again with slope. Find the slope of (1,3) and (7,-6)

Vertical and Horizontal

Write and equation for the vertical and horizontal lines passing through the point (4,-4) in (x,y) coordinates. Please show the steps to help me understand how you accomplished this.

Line Equations from a Word Problems

Sue owens her brother $8000 and agrees to pay $250 a month until it is paid off. Let A represent the amount owed(in dollars) and let N represent the number of payments made. Write an equation relating A to N and then graph your equation using the the Y axis as A with a scale of 1000 to 8000 and the x axis represents N with a s

Graph from a Word Problem

Joe is saving money. He saves $50 in his piggy bank to start with and adds an additional $10 each month. Let A represent the total amount of money (in dollars) in the piggy bank and let N represent the number of months that Joe has been saving. Write an equation relating A to N and then graph the equation using the axis Y for

Graphing Word Problems

Kira owes $6125 and agrees to pay $175 a month until paid. Let A represent the amount owed (in dollars) and let N represent the number of payments made. Write an equation relating A to N then graph the equation. State the points being graphed.

Writing Equations and Graphing

Lisa is a software saleswoman. Lisa's monthly salary is $1700 plus an additional $90 for every copy of Math is Fun she sells. Let S represent Lisa's monthly salary (in dollars), and let N represent the number of copies of Math is Fun that she sold. Write an equation relating S to N, and then graph your equation using the axes

Point of Inflection

Please see the attached file for the fully formatted problems. Let . Which value of t corresponds to an inflection point for f(t)? A. B. C. D. There is no inflection point.

Ordered Pairs

Complete the given ordered pairs so tht each ordered pair satisfies the given equation X + 2y = 1: (0, ), (-2, ), (2, )

X and y components

Please help! I just need the answers. No free body diagram either. Thanks.

Connected and Continuous

There are a couple of concepts I need clarification for: 1) If a set has no interior points, then is it necessarily closed? Isn't the empty set considered open? 2) If the graph of f: R -> R is connected, does it have to be continuous? In just Real -> Real aren't these definitions equivalent? Thanks.

If G is regular of degree

Assume that G does not equal K_2. K_2 is the complete 2-partite graph If G is regular of degree "r" and Kappa(G) = 1, prove that &#955;(G) <= [floor function of "r / 2" ] The floor function, also called the greatest integer function or integer value, gives the largest integer less than or equal to "r / 2." DEFN: the

Increasing and Decreasing Functions

2. (2--6) Determine the intervals on which the function is decreasing and increasing and then find local minima and maxima. 3. 4. 5. 6. The graph of is located below the X-axis but it touches the -axis at . What can you say about the graph of ? Please see the attached file for the fully formatted problems.