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<title>Spring 08, Math 107, Practice Mini Test 2</title>
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<center>Spring 108, Math 107</center>
<center>Practice Mini Test #2</center>
<br/>


<math xmlns='http://www.w3.org/1998/Math/MathML'>
</math>
<br/>1. Find the x and y-intercepts of the graph of the function
<math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mo stretchy='false'>(</mo><mi>x</mi><mo>&#x2212;</mo><mn>1</mn><mo stretchy='false'>)</mo><mo stretchy='false'>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo stretchy='false'>)</mo><mo stretchy='false'>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo stretchy='false'>)</mo>
  </mrow>
</math> (<a href="spring08-math107-practice-test2-1.asp">Solution</a>)
<br/><br/>2. Find the x and y-intercepts of the graph of the function
<math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mn>2</mn><msup>
    <mi>x</mi>
    <mn>2</mn>
   </msup>
   <mo>&#x2212;</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>1</mn>
  </mrow>
</math> (<a href="spring08-math107-practice-test2-2.asp">Solution</a>)
<br/><br/>3. Find the point of intersection of the graph of the function 
<math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><msup>
    <mi>x</mi>
    <mn>2</mn>
   </msup>
   <mo>&#x2212;</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn>
  </mrow>
</math> and
<math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mi>x</mi><mo>&#x2212;</mo><mn>4</mn>
  </mrow>
</math> (<a href="spring08-math107-practice-test2-3.asp">Solution</a>)
<br/><br/>4. Find the slope of the line passing through the points (2,-3) and (-1,1).
(<a href="spring08-math107-practice-test2-4.asp">Solution</a>)
<br/><br/>5. Find the equation of the line passing through the point (2,-1) and having slope = -1.
(<a href="spring08-math107-practice-test2-5.asp">Solution</a>)
<br/><br/>6. Find the equation of the line passing through the point (-2,3) and perpendicular to the line x = 2y + 3.
(<a href="spring08-math107-practice-test2-6.asp">Solution</a>)
<br/><br/>7. <math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <munder>
    <mrow>
     <mi>lim</mi><mo>&#x2061;</mo>
    </mrow>
    <mrow>
     <mi>x</mi><mo>&#x2192;</mo><mo>&#x2212;</mo><mn>3</mn>
    </mrow>
   </munder>
   <mtext>&#160;</mtext>
   <mn>2</mn><msup>
    <mi>x</mi>
    <mn>2</mn>
   </msup>
   <mo>&#x2212;</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>4</mn>
  </mrow>
</math> (<a href="spring08-math107-practice-test2-7.asp">Solution</a>)
<br/><br/>8. Find <math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <munder>
    <mrow>
     <mi>lim</mi><mo>&#x2061;</mo>
    </mrow>
    <mrow>
     <mi>x</mi><mo>&#x2192;</mo><mo>&#x2212;</mo><mn>1</mn>
    </mrow>
   </munder>
   <mtext>&#160;</mtext>
   <mfrac>
    <mrow>
     <mi>x</mi><mo>+</mo><mn>1</mn>
    </mrow>
    <mrow>
     <msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <mo>&#x2212;</mo><mi>x</mi><mo>+</mo><mn>3</mn>
    </mrow>
   </mfrac>
   
  </mrow>
</math> (<a href="spring08-math107-practice-test2-8.asp">Solution</a>)

<br/><br/>9. Find <math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <munder>
    <mrow>
     <mi>lim</mi><mo>&#x2061;</mo>
    </mrow>
    <mrow>
     <mi>x</mi><mo>&#x2192;</mo><mo>&#x2212;</mo><mn>2</mn>
    </mrow>
   </munder>
	<mtext>&#160;</mtext>
  <mfrac>
    <mrow>
     <msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <mo>+</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn>
    </mrow>
    <mrow>
     <msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <mo>+</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>6</mn>
    </mrow>
   </mfrac>
   
  </mrow>
</math>. (<a href="spring08-math107-practice-test2-9.asp">Solution</a>)



<br/><br/>10. Find the domain of the function
<math xmlns='http://www.w3.org/1998/Math/MathML'>
  <mrow>
   <mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mfrac>
    <mrow>
     <msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <mo>&#x2212;</mo><mn>9</mn>
    </mrow>
    <mrow>
     <mi>x</mi><mo>&#x2212;</mo><mn>3</mn>
    </mrow>
   </mfrac>
   
  </mrow>
</math>. Draw the graph of this function. Is this function continuous? (<a href="spring08-math107-practice-test2-10.asp">Solution</a>)










 


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<hr/>Copyright &#169; Dayal D. Purohit, Ph.D.(Mathematics)
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