1. Use the graph to find f(5)2. What is the value of x when f(x) =100? EXAMPLE 7 Analyzing the Graph of a FunctionThe human immunodeficiency virus, or HIV, infects and kills helper T cells. BecauseT cells stimulate the immune system to produce antibodies, their destructiondisables the body's defenses against other pathogens. By counting the number ofT cells that remain active in the body, the progression of HIV can be monitored.The fewer helper T cells, the more advanced the disease. Figure 2.9 shows a graphthat is used to monitor the average progression of the disease. The average numberof T cells, f(x), is a function of time after infection, x.yT Cell Count and HIV Infection1200Asymptomatic StageFew or no symptoms present.1000800Symptomatic StageSymptoms begin or* 600get worse.AIDS ClinicalDiagnosis400200y = flx)1 23 4 5 6 7 86.10 11Time after Infection (years)FIGURE 2.9Source: B. E. Pruitt et al., Human Sexuality, Prentice Hall, 2007.a. Explain why f represents the graph of a function.b. Use the graph to find and interpret f(8).c. For what value of x is f(x) = 350?d. Describe the general trend shown by the graph.Average T Cell Count(per milliliter of blood)

From the graph shown in the figure. At x = 5 the y coordinate is 400. Hence f(5) = 400

y T Cell Count and HIV Infection 1200 Asymptomatic Stage Few or no symptoms present. 1000 800 Symptomatic Stage Symptoms begin or get worse. 600 400 AIDS Clinical Diagnosis 200 y = f(x) 1 2 3 4 6 7 8 9 10 11 Time after Infection (years) Average T Cell Count (per milliliter of blood)

y T Cell Count and HIV Infection 1200 Asymptomatic Stage Few or no symptoms present. 1000 800 Symptomatic Stage Symptoms begin or get worse. 600 400 AIDS Clinical Diagnosis 200 y = f(x) 1 2 3 4 6 7 8 9 10 11 Time after Infection (years) Average T Cell Count (per milliliter of blood)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: 70. What is the domain of the function f(x) = Vx - 3x?

A: Consider the function, f(x)=x3-3x2 Domain of a function y=f(x) is the set of all x-values for which…

Q: Q1. If g(4) = -9 for a function g(x), what can you say about g¬'(-9) ?

Q: Find the domain and range a V4 - x2, h(x) =

A: Find the domain and range and sketch the graph of the function h(x)=4-x2

Q: 16. Graph the function f(x) = -3x + 7.

A: The given function is: fx=-3x+7 This is a linear function, which represents the line. To graph, this…

Q: Graph each pair of functions. A g(x) = 2px" and h(x) = Complete the table of values and use it to…

Q: 3. The function f(x) is represented as a graph. Use f(x) to answer the following questions: a.…

A: Given, graph

Q: Compare the of f(x) = 3x.

A: Given, The function is jx=3x+3.To find : Compare the graph of the given function to the…

Q: 5. Graph the function: f(x) = {,2 s-4x – 3 for x < 0 for x 2 0

A: Note: As per Bartleby rule, only one question can be solved at a time. So, kindly post other…

Q: 2. How does the value of k affect the graph of f(x) = (x- h) + k?

Q: Speed Limit (in mph) Ay 80 70 60- 50- 40- 30- 20- 10 *** -co 11

Q: 13. Is the following the graph of a function? Why or why not? 14. For the function f(x) = x² + 5x –…

Q: 4. Input the table of values here f(x) = x f (x) -D2 -2 -1 What do you notice about the y values…

A: Topic:- function

Q: Below is the graph of a function f(x). On the same set of axes, graph f-1(x).

A: Take the square box in graph has one unit. Then, given f(x) plot becomes…

Q: Examine the graph of the function f(x) 10x+3x-12r. %3D

A: Given f(x)=10x3+3x2-12x

Q: 3. 1. f(x)= X-4

Q: 4. For the function f(x) = *= x+1 (a) Find f(0) (b) Find f(-4) (c) Find f(4) What point is on the…

A: I have explained everything with in the solution .please go through that.

Q: 5. f(x) = (x+3)²(x-2)(x+1)- continued e) Graph the function. f) Determine the domain and range of…

A: Ok

Q: Consider f(x) = 3 x . Describe how the graph of each function compares to f. 8. g(x) = 3 x + 4 9.…

A: Sol:- For each of the given functions, we can compare the graph to the graph of f(x) = 3x by…

Q: 6- 4- y 2- shows the graph of the function f(x) =

A: Given: The graph shown above is the function of inverse hyperbolic function of tanh-1x

Q: Q3. If g(1) = -3 for a function g(x), what can you say about g -3)

Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

Question

1. Use the graph to find f(5)

2. What is the value of x when f(x) =100?

EXAMPLE 7 Analyzing the Graph of a Function
The human immunodeficiency virus, or HIV, infects and kills helper T cells. Because
T cells stimulate the immune system to produce antibodies, their destruction
disables the body's defenses against other pathogens. By counting the number of
T cells that remain active in the body, the progression of HIV can be monitored.
The fewer helper T cells, the more advanced the disease. Figure 2.9 shows a graph
that is used to monitor the average progression of the disease. The average number
of T cells, f(x), is a function of time after infection, x.
y
T Cell Count and HIV Infection
1200
Asymptomatic Stage
Few or no symptoms present.
1000
800
Symptomatic Stage
Symptoms begin or
* 600
get worse.
AIDS Clinical
Diagnosis
400
200
y = flx)
1 2
3 4 5 6 7 8
6.
10 11
Time after Infection (years)
FIGURE 2.9
Source: B. E. Pruitt et al., Human Sexuality, Prentice Hall, 2007.
a. Explain why f represents the graph of a function.
b. Use the graph to find and interpret f(8).
c. For what value of x is f(x) = 350?
d. Describe the general trend shown by the graph.
Average T Cell Count
(per milliliter of blood)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ellipses$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

2. Lijah opened an account at Advantis Credit Union. The balance of her account after x years is represented by the function b(x) = 500(1.05)*. What annual interest rate is Lijah earning? а. b. After how many years did it take for Lijah's balance to double? Show all of your work.
What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x+8)? A. Shifted up B. Shifted left C. Shifted Right D. Shifted down
In this example we consider the function W= f(T,v) where W is the wind-chill index, T is the actual temperature, and v is the wind speed. A numerical representation is given in this table. Need help with d and e
1. State the increasing and decreasing interval from the graph below: y = f(x) 3 2- -1 2. State whether this functions are even, odd or neither. a) f(x) = x + b) f(x) = 3x³ + 2x²
14. Graph the function f(x)=-5+2Vx+3 on the grid below. Show the table you created by hand or using your calculator. y State the range of this function.
# 2. Determine if the function g(x) = 3x+5 x is even, odd, or neither (a) using algebraic approach, (b) using the graph of g. Explain all your conclusions.
1. The Salt Lake City urban forest now consists of about 90,000 public trees. The urban forestry department plans to increase the number of trees by 2500 every four years. (1.1) Write a function f(x) this gives the number of public trees after x years. (1.2) (1.3) Answer: Based on this function, how many trees will there be in ten years? Answer: Based on this function, after how many years will there be 130,000 trees?