Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Chapter 1, Problem 74SGR
To determine

To identify: The whether the graph provided below is linear or not. Also compute and interpret the intercepts, symmetry, positive, negative, increasing, decreasing and the x -coordinate of any relative extrema and end the end behavior of the graph.

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 1, Problem 74SGR , additional homework tip 1

Expert Solution & Answer
Check Mark

Answer to Problem 74SGR

The graph is non-linear. The y -intercept (0,60000)is and there is no x -intercept. The graph is always positive. There is no symmetry. The graph is both increasing when x is between 1980 and 2000also when x is between 2005 and 2015and decreasing when x is between 2000 and 2005. Relative maximum at point x=2000and relative minima at the point x=2005. The end behavior of the graph is the number of patents increased between the years 2010 and 2015.

Explanation of Solution

Given information:

The graphical representation of number of U.S. Patents granted from the year 1980 to 2015.

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 1, Problem 74SGR , additional homework tip 2

Formula used:

The graph of a function is said to be linear is it is straight line. If it is a curve it is non-linear.

The x- intercepts are the points on x -axis where the graph of the equation intersects the x -axis.

The y- intercepts are the points on y -axis where the graph of the equation intersects the y -axis.

When the graph of the function lies above the x -axis the function is said to be positive otherwise negative.

When the graph of the function goes up it is an increasing function when viewed from left to right otherwise function is decreasing.

The function has relative high and low values of function. A function has relative minimum when no other near by point has a lesser y -coordinate. A function has relative maximum when no other near by point has a greater y -coordinate.

End behavior of the graph represents the values of the function at positive and negative extremes in domain of the function.

Calculation:

Consider the graphical representation of number of U.S. Patents granted from the year 1980 to 2015.

  Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018, Chapter 1, Problem 74SGR , additional homework tip 3

The x -axis denote the years and y -axis denote the number of patents in thousands.

Recall that the graph of a function is said to be linear is it is straight line. If it is a curve it is non-linear.

Observe that graph is not a straight line so it is a non-linear graph.

Also the graph of the function is not divided by any line into mirror images, so it is not symmetric also.

Recall that the x- intercepts are the points on x -axis where the graph of the equation intersects the x -axis.

Observe that the graph does not intersect the x -axis so there are no x -intercepts.

The y- intercepts are the points on y -axis where the graph of the equation intersects the y -axis.

Observe that the graph intersects the y -axis at the point (0,60000) that is number of patents in the year 1980 were around 60,000.

Recall that when the graph of the function lies above the x -axis the function is said to be positive otherwise negative.

Observe that graph of the function always lie above the x -axisso the function is said to be positive that is number of patents is always a positive number.

Recall that when the graph of the function goes up it is an increasing function when viewed from left to right otherwise function is decreasing.

When value of x lie between 1980 and 2000 also between 2005 and 2015 the function is increasing, the number of patents increase between the years 1980 and 2000 also between 2005 and 2015. The function decreasing when x lie between 2000 and 2005 that is number of patents decreased during that year.

Recall that the function has relative high and low values of function. A function has relative minimum when no other near by point has a lesser y -coordinate. A function has relative maximum when no other near by point has a greater y -coordinate.

At x=2000 the graph has relative maximum and at x=2005 the graph has relative minimum. That is number of patents were high in year 2000 and low in the year 2005.

Recall that the end behavior of the graph represents the values of the function at positive and negative extremes in domain of the function.

The graph describes the number U.S patents only till the year 2015. So end behavior of the graph is predicted by the nature of graph between the year 2010 and 2015. It is observed that the graph is increasing between the years so end behavior is number of patents increased between the years 2010 and 2015.

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Chapter 1 Solutions

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Ch. 1.1 - Prob. 1AGPCh. 1.1 - Prob. 1BGPCh. 1.1 - Prob. 2AGPCh. 1.1 - Prob. 2BGPCh. 1.1 - Prob. 1CYUCh. 1.1 - Prob. 2CYUCh. 1.1 - Prob. 3CYUCh. 1.1 - Prob. 4CYUCh. 1.1 - Prob. 5CYUCh. 1.1 - Prob. 6CYU
Ch. 1.1 - Prob. 7CYUCh. 1.1 - Prob. 8CYUCh. 1.1 - Prob. 9CYUCh. 1.1 - Prob. 10CYUCh. 1.1 - Prob. 11PPSCh. 1.1 - Prob. 12PPSCh. 1.1 - Prob. 13PPSCh. 1.1 - Prob. 14PPSCh. 1.1 - Prob. 15PPSCh. 1.1 - Prob. 16PPSCh. 1.1 - Prob. 17PPSCh. 1.1 - Prob. 18PPSCh. 1.1 - Prob. 19PPSCh. 1.1 - Prob. 20PPSCh. 1.1 - Prob. 21PPSCh. 1.1 - Prob. 22PPSCh. 1.1 - Prob. 23PPSCh. 1.1 - Prob. 24PPSCh. 1.1 - Prob. 25PPSCh. 1.1 - Prob. 26PPSCh. 1.1 - Prob. 27PPSCh. 1.1 - Prob. 28PPSCh. 1.1 - Prob. 29PPSCh. 1.1 - Prob. 30PPSCh. 1.1 - Prob. 31PPSCh. 1.1 - Prob. 32PPSCh. 1.1 - Prob. 33PPSCh. 1.1 - Prob. 34PPSCh. 1.1 - Prob. 35PPSCh. 1.1 - Prob. 36PPSCh. 1.1 - Prob. 37PPSCh. 1.1 - Prob. 38HPCh. 1.1 - Prob. 39HPCh. 1.1 - Prob. 40HPCh. 1.1 - Prob. 41HPCh. 1.1 - Prob. 42HPCh. 1.1 - Prob. 43PFACh. 1.1 - Prob. 44PFACh. 1.1 - Prob. 45PFACh. 1.1 - Prob. 46PFACh. 1.1 - Prob. 47PFACh. 1.1 - Prob. 48PFACh. 1.1 - Prob. 49PFACh. 1.2 - Prob. 1AGPCh. 1.2 - Prob. 1BGPCh. 1.2 - Prob. 1CGPCh. 1.2 - Prob. 2AGPCh. 1.2 - Prob. 2BGPCh. 1.2 - 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Prob. 5PPSCh. 1.5 - Prob. 6PPSCh. 1.5 - Prob. 7PPSCh. 1.5 - Prob. 8PPSCh. 1.5 - Prob. 9PPSCh. 1.5 - Prob. 10PPSCh. 1.5 - Prob. 11PPSCh. 1.5 - Prob. 12PPSCh. 1.5 - Prob. 13PPSCh. 1.5 - Prob. 14PPSCh. 1.5 - Prob. 15PPSCh. 1.5 - Prob. 16PPSCh. 1.5 - Prob. 17PPSCh. 1.5 - Prob. 18PPSCh. 1.5 - Prob. 19PPSCh. 1.5 - Prob. 20PPSCh. 1.5 - Prob. 21PPSCh. 1.5 - Prob. 22PPSCh. 1.5 - Prob. 23PPSCh. 1.5 - Prob. 24PPSCh. 1.5 - Prob. 25PPSCh. 1.5 - Prob. 26PPSCh. 1.5 - Prob. 27HPCh. 1.5 - Prob. 28HPCh. 1.5 - Prob. 29PFACh. 1.5 - Prob. 30PFACh. 1.5 - Prob. 31PFACh. 1.5 - Prob. 32PFACh. 1.5 - Prob. 33PFACh. 1.5 - Prob. 34PFACh. 1.5 - Prob. 35PFACh. 1.6 - Prob. 1AGPCh. 1.6 - Prob. 1BGPCh. 1.6 - Prob. 2AGPCh. 1.6 - Prob. 2BGPCh. 1.6 - Prob. 3AGPCh. 1.6 - Prob. 3BGPCh. 1.6 - Prob. 1CYUCh. 1.6 - Prob. 2CYUCh. 1.6 - Prob. 3CYUCh. 1.6 - Prob. 4CYUCh. 1.6 - Prob. 5CYUCh. 1.6 - Prob. 6CYUCh. 1.6 - Prob. 7CYUCh. 1.6 - Prob. 8CYUCh. 1.6 - Prob. 9PPSCh. 1.6 - Prob. 10PPSCh. 1.6 - Prob. 11PPSCh. 1.6 - Prob. 12PPSCh. 1.6 - Prob. 13PPSCh. 1.6 - Prob. 14PPSCh. 1.6 - Prob. 15PPSCh. 1.6 - Prob. 16PPSCh. 1.6 - Prob. 17PPSCh. 1.6 - Prob. 18PPSCh. 1.6 - Prob. 19PPSCh. 1.6 - Prob. 20PPSCh. 1.6 - Prob. 21PPSCh. 1.6 - Prob. 22PPSCh. 1.6 - Prob. 23PPSCh. 1.6 - Prob. 24PPSCh. 1.6 - Prob. 25PPSCh. 1.6 - Prob. 26PPSCh. 1.6 - Prob. 27PPSCh. 1.6 - Prob. 28PPSCh. 1.6 - Prob. 29PPSCh. 1.6 - Prob. 30PPSCh. 1.6 - Prob. 31PPSCh. 1.6 - Prob. 32PPSCh. 1.6 - Prob. 33PPSCh. 1.6 - Prob. 34PPSCh. 1.6 - Prob. 35PPSCh. 1.6 - Prob. 36PPSCh. 1.6 - Prob. 37PPSCh. 1.6 - Prob. 38HPCh. 1.6 - Prob. 39HPCh. 1.6 - Prob. 40HPCh. 1.6 - Prob. 41HPCh. 1.6 - Prob. 42HPCh. 1.6 - Prob. 43PFACh. 1.6 - Prob. 44PFACh. 1.6 - Prob. 45PFACh. 1.6 - Prob. 46PFACh. 1.6 - Prob. 47PFACh. 1.7 - Prob. 1GPCh. 1.7 - Prob. 2GPCh. 1.7 - Prob. 3AGPCh. 1.7 - Prob. 3BGPCh. 1.7 - Prob. 4AGPCh. 1.7 - Prob. 4BGPCh. 1.7 - Prob. 4CGPCh. 1.7 - Prob. 4DGPCh. 1.7 - Prob. 5AGPCh. 1.7 - Prob. 5BGPCh. 1.7 - Prob. 5CGPCh. 1.7 - Prob. 5DGPCh. 1.7 - Prob. 1CYUCh. 1.7 - Prob. 2CYUCh. 1.7 - Prob. 3CYUCh. 1.7 - Prob. 4CYUCh. 1.7 - Prob. 5CYUCh. 1.7 - Prob. 6CYUCh. 1.7 - Prob. 7CYUCh. 1.7 - Prob. 8CYUCh. 1.7 - Prob. 9CYUCh. 1.7 - Prob. 10CYUCh. 1.7 - Prob. 11CYUCh. 1.7 - Prob. 12CYUCh. 1.7 - Prob. 13CYUCh. 1.7 - Prob. 14CYUCh. 1.7 - Prob. 15CYUCh. 1.7 - Prob. 16CYUCh. 1.7 - Prob. 17CYUCh. 1.7 - Prob. 18CYUCh. 1.7 - Prob. 19CYUCh. 1.7 - Prob. 20PPSCh. 1.7 - Prob. 21PPSCh. 1.7 - Prob. 22PPSCh. 1.7 - Prob. 23PPSCh. 1.7 - Prob. 24PPSCh. 1.7 - Prob. 25PPSCh. 1.7 - Prob. 26PPSCh. 1.7 - Prob. 27PPSCh. 1.7 - Prob. 28PPSCh. 1.7 - Prob. 29PPSCh. 1.7 - Prob. 30PPSCh. 1.7 - Prob. 31PPSCh. 1.7 - Prob. 32PPSCh. 1.7 - Prob. 33PPSCh. 1.7 - Prob. 34PPSCh. 1.7 - Prob. 35PPSCh. 1.7 - Prob. 36PPSCh. 1.7 - Prob. 37PPSCh. 1.7 - Prob. 38PPSCh. 1.7 - Prob. 39PPSCh. 1.7 - Prob. 40PPSCh. 1.7 - Prob. 41PPSCh. 1.7 - Prob. 42PPSCh. 1.7 - Prob. 43PPSCh. 1.7 - Prob. 44PPSCh. 1.7 - Prob. 45PPSCh. 1.7 - Prob. 46PPSCh. 1.7 - Prob. 47PPSCh. 1.7 - Prob. 48PPSCh. 1.7 - Prob. 49HPCh. 1.7 - Prob. 50HPCh. 1.7 - Prob. 51HPCh. 1.7 - 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Prob. 7MCQCh. 1 - Prob. 8MCQCh. 1 - Prob. 9MCQCh. 1 - Prob. 10MCQCh. 1 - Prob. 11MCQCh. 1 - Prob. 12MCQCh. 1 - Prob. 13MCQCh. 1 - Prob. 14MCQCh. 1 - Prob. 15MCQCh. 1 - Prob. 16MCQCh. 1 - Prob. 17MCQCh. 1 - Prob. 18MCQCh. 1 - Prob. 19MCQCh. 1 - Prob. 20MCQCh. 1 - Prob. 21MCQCh. 1 - Prob. 22MCQCh. 1 - Prob. 23MCQCh. 1 - Prob. 24MCQCh. 1 - Prob. 25MCQCh. 1 - Prob. 1SGRCh. 1 - Prob. 2SGRCh. 1 - Prob. 3SGRCh. 1 - Prob. 4SGRCh. 1 - Prob. 5SGRCh. 1 - Prob. 6SGRCh. 1 - Prob. 7SGRCh. 1 - Prob. 8SGRCh. 1 - Prob. 9SGRCh. 1 - Prob. 10SGRCh. 1 - Prob. 11SGRCh. 1 - Prob. 12SGRCh. 1 - Prob. 13SGRCh. 1 - Prob. 14SGRCh. 1 - Prob. 15SGRCh. 1 - Prob. 16SGRCh. 1 - Prob. 17SGRCh. 1 - Prob. 18SGRCh. 1 - Prob. 19SGRCh. 1 - Prob. 20SGRCh. 1 - Prob. 21SGRCh. 1 - Prob. 22SGRCh. 1 - Prob. 23SGRCh. 1 - Prob. 24SGRCh. 1 - Prob. 25SGRCh. 1 - Prob. 26SGRCh. 1 - Prob. 27SGRCh. 1 - Prob. 28SGRCh. 1 - Prob. 29SGRCh. 1 - Prob. 30SGRCh. 1 - Prob. 31SGRCh. 1 - Prob. 32SGRCh. 1 - Prob. 33SGRCh. 1 - Prob. 34SGRCh. 1 - Prob. 35SGRCh. 1 - Prob. 36SGRCh. 1 - Prob. 37SGRCh. 1 - Prob. 38SGRCh. 1 - Prob. 39SGRCh. 1 - Prob. 40SGRCh. 1 - Prob. 41SGRCh. 1 - Prob. 42SGRCh. 1 - Prob. 43SGRCh. 1 - Prob. 44SGRCh. 1 - Prob. 45SGRCh. 1 - Prob. 46SGRCh. 1 - Prob. 47SGRCh. 1 - Prob. 48SGRCh. 1 - Prob. 49SGRCh. 1 - Prob. 50SGRCh. 1 - Prob. 51SGRCh. 1 - Prob. 52SGRCh. 1 - Prob. 53SGRCh. 1 - Prob. 54SGRCh. 1 - Prob. 55SGRCh. 1 - Prob. 56SGRCh. 1 - Prob. 57SGRCh. 1 - Prob. 58SGRCh. 1 - Prob. 59SGRCh. 1 - Prob. 60SGRCh. 1 - Prob. 61SGRCh. 1 - Prob. 62SGRCh. 1 - Prob. 63SGRCh. 1 - Prob. 64SGRCh. 1 - Prob. 65SGRCh. 1 - Prob. 66SGRCh. 1 - Prob. 67SGRCh. 1 - Prob. 68SGRCh. 1 - Prob. 69SGRCh. 1 - Prob. 70SGRCh. 1 - Prob. 71SGRCh. 1 - Prob. 72SGRCh. 1 - Prob. 73SGRCh. 1 - Prob. 74SGRCh. 1 - Prob. 75SGRCh. 1 - Prob. 1PTCh. 1 - Prob. 2PTCh. 1 - Prob. 3PTCh. 1 - Prob. 4PTCh. 1 - Prob. 5PTCh. 1 - Prob. 6PTCh. 1 - Prob. 7PTCh. 1 - Prob. 8PTCh. 1 - Prob. 9PTCh. 1 - Prob. 10PTCh. 1 - Prob. 11PTCh. 1 - Prob. 12PTCh. 1 - Prob. 13PTCh. 1 - Prob. 14PTCh. 1 - Prob. 15PTCh. 1 - Prob. 16PTCh. 1 - Prob. 17PTCh. 1 - Prob. 18PTCh. 1 - Prob. 19PTCh. 1 - Prob. 20PTCh. 1 - Prob. 21PTCh. 1 - Prob. 1PFACh. 1 - Prob. 2PFACh. 1 - Prob. 3PFACh. 1 - Prob. 4PFACh. 1 - Prob. 5PFACh. 1 - Prob. 6PFACh. 1 - Prob. 7PFACh. 1 - Prob. 8PFACh. 1 - Prob. 9PFACh. 1 - Prob. 10PFACh. 1 - Prob. 11PFACh. 1 - Prob. 12PFACh. 1 - Prob. 13PFACh. 1 - Prob. 14PFACh. 1 - Prob. 15PFA

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY