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# Graphs and Functions

### Graphs and Linear Equations

Section 3.1 Use the given equation to find the missing coordinates in the following tables: 34. X Y -2 0 2 -3 -7 Graph each equation. Plot at least five points for each equation. Use graph paper. See Examples 3.5. If you have a graphing calculator, use it to check your graphs when possible.

### Graphs of Exponential and Logarithmic Functions

Jelp with plotting the graph with the following functions? 1) f(x)=6^x 2) f(x)=3^x-2 3) f(x)=(1/2)^x 4) f(x)=log2 x

### Equations and Graphing problems

Please show work so that I may understand. Thank you. 1.) Solve the equation x + 0.04x = 9600 2.) Solve the inequality (1/6) x - 1 &#8804; 4 + (1/3) x. Express answer in both graphical and interval notation form. Find the missing coordinates y = -x + 4 x y -2 0 2 0 -2 3.) Plot

### Graphing and Functions

1. Suppose I had a lemonade stand. When I charge \$1, I sold 50 cups, when I raised the price to \$2, I only sold 25 cups. Write an equation for the number of cups I sold as a function of the price i charged. Denote C for number of cups and P for price. Assume the function is linear. 2. Write an equation for f(x) based on x -2,

### Maximum Value of a Function and Decreasing Function

In recession, congress decided to stimulate the economy by providing funds to hire unemployed workers for gov. projects. Suppose the t months after the stimulus programs have begun, there are N(t) thousand people unemployed, where: N(t)= -t^3 + 45t^2+408t + 3078 a). What is the max # of unemployed workers? When d

Look at the graph above and comment on the sign of D or the discriminant. Form the quadratic equation based on the information provided and find its solution. (-1,0) (-0.16,-2) (0.67,0) use y=ax^2+ b+c also But if we know the roots x1 and x2 of a quadratic equation, we can write the equation in a completely equivalen

### Discriminants

I am having trouble understanding the sign of the discriminant in quadratic equations. I'm confused. See attached for my full problem.

### Slope-Intercept Form

Please show work so that I can understand how you arrive at your answer. Thank you. 1.) Write the equation in slope intercept form y + 2 = - 6(x-1) 2.) Determine the equation of each line. Write the answer in slope intercept form. The line through (4,0) that is perpendicular to the line x + y = 3 Solve

### Outerplanar Graphs

A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. Prove the following: If G = G(p, q) is outerplanar with p >= 2, then q <= 2p - 3.

### Outerplanar and Bipartite Graphs

A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. A graph G is outerplanar iff G + K_1 is planar. Note:A bipartite graph (i.e., a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent

### Graphs and the Time Value of Money

Please take this real-life situation: I currently have a CD investment accounts in the Dominican Republic. I invested \$10,000 (\$M) in The Central Bank of the Dominican Republic. This investment account produced a simple annual interest of 10% (R) for me. I plan to leave my money in this investment account for (X) amount of year

### Which of the following represents a straight-line graph?

Please see attached file for full problem description. Which of the following represents a straight-line graph? a. none of the following is a straight-line graph b. all of the following are straight-line graphs c. varX varY 1 6 2 4 3 2 d. varW varZ 3 8 4 7 5 4 e. varT varU 10 0.5 11 1.5 12 2 Wh

### Sketch a possible graph of the velocity.

An object is moving along the straight line as follows. It starts at x = 0 and then it moves to the right to x = 2. Then the object moves to the left to x = - 3, and finally to the right to stop at x = 1. Sketch a possible graph of the position function s(t). Sketch a possible graph of the velocity v(t) (the instantaneous rate o

### Graphing, Trends and Forecasting

Please see the attached file for the complete questions. Complete the ordered pairs so that each is a solution for the given equation. 24. (0, ), ( , ), ( ,0), ( , ) 46. Science and medicine. Celsius temperature readings can be converted to Fahrenheit readings using the formula . What is the Fahrenheit tempera

### Graphing and Linear Equations

Please see the attached file for the complete questions. MTH 212 Unit 2 - Individual Project A 1. The following table shows the number of hours five car salespeople worked and the number of cars they sold. Using Excel, plot each point on the same graph where the first coordinate is the number of hours and the second coord

### Modelling Data with Polynomial and Rational Functions

Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the gas required varies as (V1/V2), raised to the third power, (V1/V2)3. Rational functions are also useful. For examp

### Cost Functions Percentages

The annual cost in dollars for removing p% of the toxic chemicals from a town's water supply is given by the following formula: C(p) = 500,000/ 100 - P a. Use the formula to determine the cost for removing 90% , 95% , and 99.5% of the toxic chemicals. b. What happens to the cost as the percentage of pollutants removed approaches

### Applications of Graphing and Derivatives : Critical Points

Using a calculator or computer, graph the functions. Describe briefly in words the interesting features of the graph including the location of the critical points and where the function in increasing/decreasing. Then use the derivative and algebra to explain the shape of the graph. 9. Try graphing the x values from -5 t

### Applications of Graphs of Linear Equations

Name: __________________________ Date: _____________ 1. Which of the ordered pairs (6, 1), (8, 0), (4, -2), (-4, 6) are solutions for the equation x + 2y = 8? 2. A small company did a poll of how their employees commuted to work. The data is shown in the bar graph below. (a) How many people commute to work v

### Graceful Trees and Paths

A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct elements from the set {0,1,...,q} in such a way that the induced edge labeling, which assigns the integer |i - j| to the edge ij, assigns the labels 1,2,...,q to the q edges of G. The graceful tree conjecture states that every tree i

### Rates of Change and Secant Lines

Please see the attached file for the fully formatted problems. 1. Let . Tabulate the change of over the intervals (i) , (ii) , (iii) , (iv) , (v) . Graph together with the secant line passing through and . Estimate how quickly is changing at .

### Where is f(x) decreasing?

Given f(x) = x^3 + x^2 - 5x +2, on what interval(s) is it decreasing?

### Eulerian Graphs: Odd or Even Vertices

Let G be a graph. The line graph L(G) of G is defined to be the graph whose vertices are the edges of G and where two vertices of L(G) are adjacent if the corresponding edges of G are adjacent. Prove that if G is connected, then L(G) is eulerian if vertices of G are all odd or all even.

### Functions and Their Graphs

Please see the attachment below for problems. I figured out number 1 and 2. I don't understand the rest of them.

### College Algebra

O For noninteger answers, please write your answer as a fraction rather than a decimal. To show your work, you will need to include o the algebra used to compute the solution to any equations. o the formula with substituted values. o the final calculated answer with units. 1) State the doma

### Functions and Their Graphs

See attached file for full problem description.

### Polynomial Functions: Graphing different linear functions and comparing them

Your manager is very pleased with your presentations and being able to show your calculations in a detailed fashion. He has asked that you help him prepare for the upcoming company summit. Before you get together, he has asked that you give him a little review on polynomial functions and how you would apply them to everyday use.

### Vertex of a Parabola

I need to understand how to find the vertex of a parabola two ways. Show examples

### Write the Objective Function

Let M be the number of units to make and B be the number of units to buy. If it costs \$2 to make a unit and \$3 to buy a unit and 4000 units are needed, the objective function is: Max 2M + 3B Min 4000 (M + B) Max 8000M + 12000B Min 2M + 3B.