True or false:
7. The points of inflection are found by solving the first derivative equal to Zero
8. When the denominator of a rational function is zero the function will always have a vertical asymptote
9. To determine the behavior of a function near the vertical asymptotes we use left and right-hand limits.
10. Determining if a local extrema is a maximum or minimum cannot be done using the second derivative test
11.A function can never cross asymptotes
12.To determine the end behavior of a function we must check the lim x-> -/+ infinity
![_7. The points of inflection are found by solving the first derivative equal to zero.<br>8. When the denominator of a rational function is zero the function will always<br>have a vertical asymptote.<br>9. To determine the behavior of a function near the vertical asymptotes we use left<br>and right hand limits.<br>10. Determining if a local extrema is a maximum or minimum cannot be done<br>using the second derivative test.<br>11. A function can never cross asymptotes.<br>12. To determine the end behavior of a function we must check the lim<br>13. Sketch a graph of a rational function that satisfies the following conditions [4 Marks]<br>f(0) = 0, f(-4) = 2, f(4) = -2<br>f(x) is undefined for x =+2<br>y<br>op<br>f (-4) = f (0) = f '(4) = 0<br>f'(x)<0 for x< -4, x>4<br>f (x) > 0 for -4 <x< -2, -2 <x<0 and<br>0 <x<2, 2 < 4<br>f](https://s3.us-east-1.amazonaws.com/storage.unifolks.com/qimg-008/008_pmysx50-r5nsptbl.jpeg)
0 for x < -2,=""><><2 f"(x)="">< 0="" for="" -2=""><><0, x=""> 2 -6 6 "/>
Extracted text: _7. The points of inflection are found by solving the first derivative equal to zero. 8. When the denominator of a rational function is zero the function will always have a vertical asymptote. 9. To determine the behavior of a function near the vertical asymptotes we use left and right hand limits. 10. Determining if a local extrema is a maximum or minimum cannot be done using the second derivative test. 11. A function can never cross asymptotes. 12. To determine the end behavior of a function we must check the lim 13. Sketch a graph of a rational function that satisfies the following conditions [4 Marks] f(0) = 0, f(-4) = 2, f(4) = -2 f(x) is undefined for x =+2 y op f (-4) = f (0) = f '(4) = 0 f'(x)<0 for="">< -4,="" x="">4 f (x) > 0 for -4 <>< -2,="" -2=""><><0 and="" 0=""><><2, 2="">< 4="" f"(0)="0" f"(x)=""> 0 for x < -2,=""><><2 f"(x)="">< 0="" for="" -2=""><><0, x=""> 2 -6 6