Domain interval for given range.pptx
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The document provides examples of determining the domain intervals where the range of functions is positive or negative based on their graphs. For a function f(x)=x^2-2x-3, the range is positive when x<-1 or x>3, and negative when -1<x<3. For -2x^2+5x+3, the range is positive when -0.5<x<3 and negative when x<-0.5 or x>3. Finally, for x^2-2x-5, the range is positive when x<-5 or x>-3, and negative when -5<x<-3.
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香港六合彩
都怕香港六合彩的嘴。似乎嘴皮薄的人才擅长能说会道，王秀的厚嘴却也擅长，可见是对人们观念的一种颠覆。呵呵。周晨晨笑着碰了一下落魄的王秀，这一碰，香港六合彩差点从凳子上掉下。香港六合彩……香港六合彩，夫唱妇随！王秀从大脑深处搜出这么一个词，听得相关的两个人脸红了半天也没人表示要为这句话追讨名誉损失。嘴里刚咬进一大口汉堡包的王峰，可谓真正的瞠目结舌。这话太刺激人，香港六合彩王秀的嘴也太拙不择言了。但汉堡包毕竟有个男子汉的汉字，又有堡垒的堡字，王峰撑开的嗓子眼开始反抗，话可不能这么说，夫唱妇随是贬义词，王秀你这是侮辱人，知道吗？就是。子允附和道，还是哥们说话在理。应该是嫁(又鸟)随(又鸟)，嫁狗随狗。子允料不到王峰会给自己留这么一手，毫无戒备地吃了个闷棍。王秀大笑，王峰却心有余悸地看着周晨晨，说完后香港六合彩才发现这话冲着香港六合彩的。其实香港六合彩根本没有瞄准目标是谁，只是想勾动板机一下，也有插句话的本意。周晨晨笑中带羞，与王峰略带歉意的目光交错。王峰见不是担心的表情，才放下悬着的心。见王峰这样开自己玩笑，子允好气又好笑，王峰用词跟王秀不同，意思却差不多。香港六合彩得报复一下，也好把王峰的话更好地融入玩笑的气氛，否则这话会未免显得太那个。香港六合彩想从王峰和王秀都姓王入手，再从秀和峰上深入，但香港六合彩两个人条件相差太多，效果上难以精彩。子允准备另辟蹊径，又苦于拘谨的王峰没留下什么破绽，香港六合彩想引诱香港六合彩，人得意忘形时才最容易出纰漏。沉默让饥饿的香港六合彩得以专心享受饱食的乐趣，子允的乐趣还在于咀嚼王秀和王峰说的话，一种朦胧的关系如果被人歪来正去地当众说开，很有种三级片女主角脱而不脱的感觉。子允喜欢这种感觉，这种情形在影视中常会出现，往往起着推波助澜作用。子允曾笑过香港六合彩傻，现在发现所谓的傻有时也有傻的妙处。不知王秀因为什么也闭上了嘴，在子允现在的印象中，好像王秀的嘴要么是说，要么是吃，反正不能又吃又说，或者吃着说着，所以香港六合彩的沉默跟赶紧吃盘子里还没吃掉多少的东西有关。王秀说话速度快，吃的速度也快。香港六合彩举起左手一看，眼皮立即抽过脂似的抬高许多，但直到咽干净嘴里的东西才说，看，十二点半了。时间真快，还有十分钟就要关校门了。子允更慌，香港六合彩还处在马老师的热点察看期。显然你是个乐观主义者，我敢说，老班已在班上点名了。王峰早可以吃完的，但越吃越慢，香港六合彩不愿吃完后看别人吃，也不愿给女生留下狼吞虎咽的印象。说过刚才那句话后，香港六合彩越想越觉得不合适，应该再说句什么缓和一下的，但当时没太意识到，想到后又不好再拿过来说。刚才的话虽说是当玩笑说的，但有失平时风格，这让香港六合彩懊恼不已。所以王秀一开口，香港六合彩便笑着接子允的茬，虽不太合时适，总算结合紧密。子允不知道王峰为什么会为自己不值得一笑的话配上这么多笑容，但也笑了笑。香港六合彩站起来看着周晨晨，香港六合彩也一笑，好像无所谓迟不迟到。这让子允安定不少，也让子允感动不小，因为这时香港六合彩越无所谓，就说明越对子允好感，越有同甘共苦的决心。那怎么办？香港六合彩怎么解释？
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- 1. Interval on domain for given values of the range.
- 2. Example 1 The graph of the function 𝑥2 − 2𝑥 − 3 is shown. State the elements of the domain for which the range of 𝑓(𝑥) is a) positive b) negative
- 3. Solution The portions shaded to the left and right of the curve and above the x-axis, represent the region where the function is positive. The corresponding x-values are 𝑥 < −1 𝑎𝑛𝑑 𝑥 > 3. Therefore the range is positive for the domain interval 𝒙 < −𝟏 𝒂𝒏𝒅 𝒙 > 𝟑.
- 4. Solution cont’d. The portions shaded within the curve and below the x-axis, represent the region where the function is negative. The corresponding x-values are 𝑥 > −1 𝑎𝑛𝑑 𝑥 < 3. Therefore the range is negative for the domain interval −1 < 𝒙 < 𝟑.
- 5. Example 2 The graph of the function −2𝑥2 + 5𝑥 + 3 is shown. State the elements of the domain for which the range of 𝑓(𝑥) is a) positive (i.e. 𝑓 𝑥 > 0) b) negative (𝑓 𝑥 < 0)
- 6. Solution The portions shaded within the curve and above the x-axis, represents the region where the function is positive. The corresponding x-values are 𝑥 > −0.5 𝑎𝑛𝑑 𝑥 < 3. Therefore the range is positive for the domain interval −𝟎. 𝟓 < 𝒙 < 𝟑.
- 7. Solution cont’d. The portion shaded to the left and right of the curve and below the x-axis, represent the region where the function is negative. The corresponding x-values are 𝑥 < −0.5 𝑎𝑛𝑑 𝑥 > 3. Therefore the range is negative for the domain interval 𝒙 < − 𝟏 𝟐 𝒂𝒏𝒅 𝒙 > 𝟑.
- 8. Example 3 The graph of the function 𝑥 + 3 𝑥 + 5 is shown. State the elements of the domain for which the range of 𝑓(𝑥) is a) positive (i.e. 𝑓 𝑥 > 0) b) negative (𝑓 𝑥 < 0) NOTE: 𝒙 + 𝟑 𝒙 − 𝟓 = 𝒙𝟐 − 𝟐𝒙 − 𝟏𝟓
- 9. Solution The portions shaded to the left and right of the curve and above the x-axis, represent the region where the function is positive. The corresponding x-values are 𝑥 < −5 𝑎𝑛𝑑 𝑥 > −3. Therefore the range is positive for the domain interval 𝒙 < −𝟓 𝒂𝒏𝒅 𝒙 > −𝟑.
- 10. Solution cont’d. The portion shaded within the curve and below the x-axis, represent the region where the function is negative. The corresponding x-values are 𝑥 > −5 𝑎𝑛𝑑 𝑥 < −3. Therefore the range is negative for the domain interval −𝟓 < 𝒙 < −𝟑.
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