Rational Functions Real World

What do you call a function of two polynomials?

• Inverse Functions

• Rational Functions

• Exponential Functions

• Logarithmic Functions

Tags

CCSS.HSF-IF.C.7D

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.

Tags

PC.F.4.5 

Abigail, Nora, and Elijah are studying rational functions in their math class. They are trying to find the horizontal asymptotes of a rational function in a real-world problem. How should they approach this task?

• They should look at the degrees of the numerator and denominator.

• They should calculate the derivative of the function.

• They should find the average of the numerator and denominator.

• They should look at the coefficients of the numerator and denominator.

Tags

PC.F.4.5 

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.

Tags

PC.F.4.5 

8694B1AFF37145BBBE5CEC3B37D5C3BB

What is the equation of the graph pictured?

Mathematical Equivalence

ON

Tags

CCSS.HSF-IF.C.7D

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.

Tags

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.

Tags

PC.F.4.5 

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.

Tags

PC.F.4.5 

Arjun is trying to find the x-intercepts of a rational function that models the profit of a company. How should he determine the x-intercepts of this function?

• Set the denominator equal to zero and solve for x.

• Set the whole function equal to zero and solve for x.

• Take the derivative of the function and find the x-values where the derivative is zero.

• Set the numerator equal to zero and solve for x.

Tags

PC.F.4.5 

Select all the following statements that are true.

• Vertical asymptote at x=1

• Vertical asymptote at x=0

• No vertical asymptote

• Hole at (-1, 0)

• Hole at (1, -1)

Tags

PC.F.4.5