Bài 3: Đồ thị của hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mo> </mo><mfenced><mrow><mi>a</mi><mo> </mo><mo>≠</mo><mn>0</mn></mrow></mfenced></math>
Hướng dẫn giải Bài 19 (Trang 52 SGK Toán 9, Tập 1)
<p><strong>Bài 19 (Trang 52 SGK Toán 9, Tập 1):</strong></p>
<p>Đồ thị của hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>3</mn></msqrt><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>3</mn></msqrt></math> được vẽ bằng compa và thước thẳng (h.8).</p>
<p>Hãy thực hiện cách vẽ đó rồi nêu lại cách thực hiện.</p>
<p><em>Áp dụng:</em> Vẽ đồ thị của hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></math> bằng compa và thước thẳng.</p>
<p><em>Hướng dẫn:</em> Tìm điểm trên trục tung có tung độ bằng <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5.</mn></msqrt></math><span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: #000000; font-family: 'Open Sans', Arial, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math>"><span id="MJXc-Node-21" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-22" class="mjx-mrow"><span id="MJXc-Node-23" class="mjx-msqrt"></span></span></span></span></p>
<p> </p>
<p><strong><span style="text-decoration: underline;"><em>Hướng dẫn giải:</em></span></strong></p>
<p>a)</p>
<p>Cho x = 0 => <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>3</mn></msqrt></math>, ta được điểm <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>;</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></math></p>
<p>Cho y = 0 => <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>3</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>=</mo><mo>></mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>ta</mi><mo> </mo><mi>được</mi><mo> </mo><mi>điểm</mi><mo> </mo><mfenced><mrow><mo>-</mo><mn>1</mn><mo>;</mo><mn>0</mn></mrow></mfenced></math></p>
<p>Để vẽ được đồ thị hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>3</mn></msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>3</mn></msqrt></math> ta cần xác định được điểm thứ 3 trên Oy.</p>
<p>Các bước vẽ đồ thị <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>3</mn></msqrt><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>3</mn></msqrt></math></p>
<p>+ Dựng điểm A(1; 1) được OA = <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math></p>
<p>+ Dựng điểm biểu diễn <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math> trên Ox: Quay một cung tâm O, bán kính OA cắt tia Ox, được điểm biểu diễn <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math>.</p>
<p>+ Dựng điểm B(<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math><span id="MathJax-Element-13-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math>"><span id="MJXc-Node-86" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-87" class="mjx-mrow"><span id="MJXc-Node-88" class="mjx-msqrt"></span></span></span><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn></mn></msqrt></math></span>; 1) được OB = <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math></p>
<p>+ Dựng điểm biểu diễn <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math><span id="MathJax-Element-15-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math>"><span id="MJXc-Node-96" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-97" class="mjx-mrow"><span id="MJXc-Node-98" class="mjx-msqrt"></span></span></span><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn></mn></msqrt></math></span>. Trên trục Oy: Quay một cung tâm O, bán kính OB cắt tia Oy, được điểm biểu diễn <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math><span id="MathJax-Element-16-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math>"><span id="MJXc-Node-101" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-102" class="mjx-mrow"><span id="MJXc-Node-103" class="mjx-msqrt"></span></span></span><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn></mn></msqrt></math></span></p>
<p>+ Vẽ đường thẳng qua điểm biểu diễn <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math> <span id="MathJax-Element-17-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math>"><span id="MJXc-Node-106" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-107" class="mjx-mrow"><span id="MJXc-Node-108" class="mjx-msqrt"></span></span></span></span>trên Oy và điểm biểu diễn -1 trên Ox ta được đồ thị hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>3</mn></msqrt><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>3</mn></msqrt></math></p>
<p><img class="wscnph" style="max-width: 100%; display: block; margin-left: auto; margin-right: auto;" src="https://static.colearn.vn:8413/v1.0/upload/library/10052022/bai-19-trand-52-sdk-toan-9-tap-1-sua2022-YwIZ2t.png" /></p>
<p>b) Áp dụng vẽ đồ thị hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cho</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>=</mo><mo>></mo><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mo>,</mo><mo> </mo><mi>ta</mi><mo> </mo><mi>ược</mi><mo> </mo><mi>điểm</mi><mo> </mo><mo>(</mo><mn>0</mn><mo>;</mo><msqrt><mn>5</mn></msqrt><mo>)</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cho</mi><mo> </mo><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>=</mo><mo>></mo><mo> </mo><msqrt><mn>5</mn></msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo> </mo><mo>=</mo><mo>></mo><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>ta</mi><mo> </mo><mi>được</mi><mo> </mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo>)</mo></math></p>
<p>Ta phải tìm điểm trên trục tung có tung độ bằng <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math></p>
<p>Cách vẽ:</p>
<p>+ Dựng điểm A (2; 1) ta được OA = <span id="MathJax-Element-24-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math>"><span id="MJXc-Node-156" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-157" class="mjx-mrow"><span id="MJXc-Node-158" class="mjx-msqrt"><span class="mjx-box"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math></span></span></span></span></span></span></span></p>
<p>+ Dựng điểm biểu diễn <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math><span id="MathJax-Element-25-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math>"><span id="MJXc-Node-161" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-162" class="mjx-mrow"><span id="MJXc-Node-163" class="mjx-msqrt"></span></span></span><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn></mn></msqrt></math></span> trên trục Oy. Quay một cung tâm O, bán kính OA cắt tia Oy, được điểm biểu diễn <span id="MathJax-Element-26-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math>"><span id="MJXc-Node-166" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-167" class="mjx-mrow"><span id="MJXc-Node-168" class="mjx-msqrt"></span></span></span><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math></mn></msqrt></math><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn></mn></msqrt></math></span>. Vẽ đường thẳng qua điểm biểu diễn <span id="MathJax-Element-27-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math>"><span id="MJXc-Node-171" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-172" class="mjx-mrow"><span id="MJXc-Node-173" class="mjx-msqrt"></span></span></span><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math></mn></msqrt></math><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn></mn></msqrt></math></span> trên Oy và điểm biểu diễn -1 trên Ox ta được đồ thị hàm số <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><msqrt><mn>5</mn></msqrt></math></p>
<p style="text-align: center;"><span class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt><mi>x</mi><mo>+</mo><msqrt><mn>5</mn></msqrt></math>"><span class="MJX_Assistive_MathML" role="presentation"><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/10052022/bai-19-trand-52-sdk-toan-9-tap-1-1-sua2022-weruEH.png" /></span></span></p>
<p><span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: #000000; font-family: 'Open Sans', Arial, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt><mi>x</mi><mo>+</mo><msqrt><mn>5</mn></msqrt></math>"><span id="MJXc-Node-11" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-12" class="mjx-mrow"><span id="MJXc-Node-13" class="mjx-msqrt"></span></span></span></span></p>
Hướng dẫn Giải Bài 19 (trang 52, SGK Toán 9, Tập 1)
GV: 
GV colearn
GV colearn
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Hướng dẫn Giải Bài 19 (trang 52, SGK Toán 9, Tập 1)
GV: GV colearn
GV colearn