首页
登录
职称英语
[img]2015m7x/ct_egreqj_egreqjs_0013_20151[/img]The figure above shows the graph
[img]2015m7x/ct_egreqj_egreqjs_0013_20151[/img]The figure above shows the graph
游客
2025-02-23
16
管理
问题
The figure above shows the graph of the function/defined by f(x)= \2x\ + 4 for all numbers x. For which of the following functions g, defined for all numbers x, does the graph of g intersect the graph of f?
选项
A、g(x)= x-2
B、g(x)= x + 3
C、g(x)= 2x-2
D、g(x)= 2x + 3
E、g(x)= 3x-2
答案
E
解析
You can see that all five choices are linear functions whose graphs are lines with various slopes and y-intercepts. The graph of Choice A is a line with slope 1 and y-intercept -2, shown in Figure 6.
It is clear that this line will not intersect the graph of f to the left of the y-axis. To the right of the y-axis, the graph of f is a line with slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y increases faster for /than for g, and therefore the graphs do not intersect to the right of the y-axis. Choice B is similarly ruled out. Note that if the y-intercept of either of the lines in Choices A and B were greater than or equal to 4 instead of less than 4, they would intersect the graph of f.
Choices C and D are lines with slope 2 and y-intercepts less than 4. Hence, they are parallel to the graph of f(to the right of the y-axis)and therefore will not intersect it. Any line with a slope greater than 2 and a y-intercept less than 4, like the line in Choice E, will intersect the graph of f(to the right of the y-axis).
The correct answer is Choice E, g(x)= 3x- 2.
This explanation uses the following strategies.
Strategy 3: Translate from an Algebraic to a Graphical Representation
Strategy 6: Add to a Geometric Figure
Strategy 8: Search for a Mathematical Relationship
转载请注明原文地址:https://tihaiku.com/zcyy/3970070.html
相关试题推荐
Itisnoteasy______theanswertothedifficultmathproblem.A、tofigureoutB
Itmakes______tofigureoutthesituationbeforetakinganyaction.A、senseB、mea
Itisnoteasy______theanswertothedifficultmathproblem.A、tofigureoutB、f
Whichofthefollowingcouldbetheequationoflinelinthefigureabove?[img]
Whatistheareaoftheshadedfigure?[img]2011q3/ct_egmatqj_egmatqchoose_0056_2
Whatistheperimeterofthefigureabove?(Note,figurenotnecessarilydrawnt
Thefigureaboverepresentsawindow,withtheshadedregionsrepresentingopeni
[img]2022m10x/ct_ve01204002j_0059_221018[/img]Inthefigureabove,segments[im
[img]2022m10x/ct_ve01204002j_0057_221018[/img]Thefigureaboveshowsthedimens
[img]2022m10x/ct_ve01204002j_0056_221018[/img]Inthefigureabove,iftheshade
随机试题
(Assoonas)(we’vefinished)supper,we’llall(gotodowntown)tosee(the)So
招标人应当根据招标项目的特点和需要编制招标文件,其内容包括( )。A.投标须知
4岁患儿,3天前突发高热,体温39.5℃,伴寒战,诉右膝部疼痛,给予抗生素治疗后
某工厂已在1周前对全厂职工作过健康检查,检查项目包括内科检查、肝功能、B超、血常
吉林省面积约19万平方千米,人口2702万。
Passage2 Thatexperiencesinfluencesu
光污染分为可见光污染和不可见光污染,下列属于不可见光污染的有( )。A:灯光污
下边四个图形中,只有一个是由上边的四个图形拼合(只能通过上、下、左、右平移)而成
下列关于中国电影著作权协会的性质描述正确的是( )。A.营利性机构 B.著作
根据《防治海洋工程建设项目污染损害海洋环境管理条例》,下列工程建设项目中不属于海
最新回复
(
0
)