• January 7th, 2019

Written Assignment 5

Paper, Order, or Assignment Requirements

For the following exercises, determine whether the relation represents y as a function of x. If the relation represents a function then write the relation as a function of x using f as the function.
x+y^2=5

For the following exercises, evaluate the function f at the indicated values f(3), f (-4), f (b), f (-b), f (a + h).
Consider the relationship7n-√5m=4.
Write the relationship as a function n= k(m).
Evaluate k(5).
Solve for k(m) = 7.

GRAPHICAL

Given the following graph
Evaluate f(4)
Solve for f(x) = 4

Numeric

For the following exercises, determine whether the relation represents a function.
{(0, 5), (-5, 8), (0, -8)}

For the following exercises, determine if the relation represented in table form represents y as a function of x.
For the following exercises, use the function f represented in table below.

x -18 -12 -6 0 6 12 18
f(x) 24 17 10 3 -4 -11 -18

Evaluate f(-6).                 
Solve f(x) = -11                
Evaluate f(12)              
Solve f(x) = -18                

For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2).
f(x) = (x^2+3x-5)/(x+2)

For the following exercises, evaluate the expressions, given functions f, g, and h:
f(x)=4x+2; g(x)=7-6x; h(x)=7x^2-3x+6

f(-1)⋅g(1)⋅h(0)         

Real-world applications

The number of cubic yards of compost, C, needed to cover a garden with area a square feet is given by  C = h(a).
A garden with area 5,000 ft2 requires 25 yd3 of compost. Express this information in terms of the function h.           
Explain the meaning of the statement h(2500) = 12.5.

3.2

Algebraic

For the following exercises, find the domain and range of each function and state it using interval notation.
f(x)=√(9-2x)/√(5x+13)

f(x)=(x+5)/(x^2-9x+14)          

GRAPHICAL

For the following exercises, write the domain and range of each function using interval notation.

Numeric

For the following exercises, given each function f, evaluate f (3), f (-2), f (1), and f (0).

Real-World Applications
The height h of a projectile is a function of the time t it is in the air. The height in meters for t seconds is given by the functionh(t)=-9.8t^2+19.6t. What is the domain of the function? What does the domain mean in the context of the problem?

The cost in euros of making x items is given by the functionC(x)=15x+750.
 The fixed cost is determined when zero items are produced. Find the fixed cost for this item.      
What is the cost of making 35 items?    
Suppose the maximum cost allowed is $2500. What are the domain and range of the cost function, C(x)?

3.3

Algebraic

For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form.
k(x)=2/(3x+1)on [2, 2+h]

Graphical

For the following exercises, use the graph of each function to estimate the intervals on which the function is increasing or decreasing.

Numeric

The table below gives the annual sales (in millions of dollars) of a product from 2008 to 2016. What was the average rate of change of annual sales (a) between 2008 and 2012, and (b) between 2010 and 2016? Round to 3 decimal places.

Year 2008 2009 2010 2011 2012 2013 2014 2015 2016
Sales (in millions) 125 132 146 165 157 151 162 188 201

For the following exercises, find the average rate of change of each function on the interval specified.
f(x)=2x^2-1on [-1, 4]

g(x)=3x^2-2/(3x^3 ) on [1, 3]       

Real-World Applications
Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=1.6t^2, where t is in seconds and d(t) is in meters. If an object is dropped from a certain height, find the average velocity of the object from t = 2 to t = 5.

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