Precalculus Complex Zeros Rational Functions

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• 15 - 12i
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• -27
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• 3 + 20i
• 3 - 20i

Lily, Evelyn, and Scarlett are studying rational functions in their math class. They come across a problem that asks, 'What is the difference between a removable and non-removable discontinuity in a rational function?' How would you explain this to them?

• A removable discontinuity can be filled by removing a value from the function at that point, like erasing a pencil mark on a graph, while a non-removable discontinuity cannot be filled by removing a value from the function at that point, like a permanent marker line on a graph.

• A removable discontinuity occurs when the function is undefined at a certain point, like a hole in a road, while a non-removable discontinuity occurs when the function is defined at a certain point, like a bridge over a river.

• A removable discontinuity can be fixed by changing the function's equation, like fixing a broken toy with a new part, while a non-removable discontinuity cannot be fixed by changing the function's equation, like a shattered vase that can't be put back together.

• A removable discontinuity can be filled by assigning a value to the function at that point, like filling a hole in a wall with plaster, while a non-removable discontinuity cannot be filled by assigning a value to the function at that point, like a window in a wall that can't be filled with plaster.

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PC.F.4.5 

Choose the correct graph that matches with the equation.

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Liam, Grace, and Harper are studying functions in their math class. Their teacher asks them to define a rational function in terms of polynomial functions. How should they respond?

• A rational function is a function that can be written as the product of two polynomial functions.

• A rational function is a function that can be written as the difference of two polynomial functions.

• A rational function is a function that can be written as the sum of two polynomial functions.

• A rational function is a function that can be written as the quotient of two polynomial functions, where the denominator is not equal to zero.

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PC.F.4.5 

Oliver and Daniel are working on a project to model the water flow through a pipe system using a rational function. How do they determine the domain of this function?

• Find the values of x that make the numerator non-zero.

• Find the values of x that make the denominator zero.

• Find the values of x that make the function undefined.

• Find the values of x that make the denominator non-zero.

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PC.F.4.5 

Lily, Michael, and Benjamin are studying rational functions in their math class. Their teacher asks them to identify an asymptote in a rational function. How would they describe it?

• A point where the graph changes direction.

• A line that the graph approaches but never touches.

• A line that the graph intersects at multiple points.

• A line that the graph touches at one point.

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PC.F.4.5 

Luna, Elijah, and Noah are trying to design a roller coaster. They need to calculate the points where the roller coaster track would go infinitely high (vertical asymptotes). How should they do this for a rational function representing the track's shape?

• They should take the derivative of the function and find the x-values where the derivative is undefined.

• They should set the numerator of the function equal to zero and solve for x.

• They should set the denominator of the function equal to zero and solve for x.

• They should set both the numerator and denominator of the function equal to zero and solve for x.

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PC.F.4.5