Graphing Rational Functions Explained

What defines a rational function?

• A function expressed as a fraction with variables in both numerator and denominator

• A function with a variable in the numerator only

• A function that can only have positive values

• A function without any discontinuities

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CCSS.HSF-IF.C.7D

What does it mean if a value is excluded in the context of rational functions?

• The function reaches its maximum at this value

• The function does not exist at this value

• The function intersects the x-axis at this value

• The function has a horizontal asymptote at this value

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CCSS.HSF-IF.C.7D

What happens to the graph of a rational function at an excluded value?

• It becomes linear

• It is undefined and may have a vertical asymptote

• It intersects the y-axis

• It reaches its maximum height

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CCSS.HSF-IF.C.7D

In the context of rational functions, what does it mean for a graph to have a break or jump?

• The function intersects itself

• The graph moves smoothly from one point to another

• The function has reached its maximum or minimum value

• The function changes direction abruptly

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CCSS.HSF-IF.C.7D

What is an asymptote in the context of rational functions?

• A line that the graph of the function approaches but never touches

• The highest point on the graph of the function

• A value that the function can touch

• A point where the function intersects the y-axis

Tags

CCSS.HSF-IF.C.7D

What does a vertical asymptote in a graph of a rational function indicate?

• The end of the graph

• A boundary the graph approaches but does not cross or touch

• The maximum value of the function

• The starting point of the graph

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CCSS.HSF-IF.C.7D

How is a vertical asymptote determined in a rational function's equation?

• By the coefficient of x in the numerator

• By the value subtracted from x in the denominator

• By the value added to x in the numerator

• By the highest exponent of x in the function

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CCSS.HSF-IF.C.7D

How can you identify a horizontal asymptote in a rational function?

• By the constant term added outside the fraction

• By finding the highest degree of x in the numerator

• By setting the denominator equal to zero

• By the coefficient of the highest degree of x in the denominator

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CCSS.HSF-IF.C.7D

What is the role of the 'a' value in the equation of a rational function?

• It determines the vertical asymptote

• It affects the curvature and distance from the asymptotes

• It sets the excluded values

• It identifies the horizontal asymptote

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CCSS.HSF-IF.C.7D

How do you graph a rational function around its asymptotes?

• By plotting points that are on the asymptotes

• By plotting points on either side of the asymptotes and drawing curves

• By only plotting points that are excluded values

• By drawing lines parallel to the asymptotes

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CCSS.HSF-IF.C.7D