Graphing Rational Functions Concepts

The video tutorial explains how to graph a rational function by identifying X and Y intercepts, vertical and horizontal asymptotes, and plotting points. It covers the calculation of intercepts, determination of asymptotes, and the analysis of the graph's behavior. The tutorial emphasizes understanding the function's behavior at intercepts and asymptotes to sketch a rough graph.

What are the key components to consider when graphing a rational function?

• Only horizontal asymptotes

• Only vertical asymptotes

• Only X and Y intercepts

• X and Y intercepts, vertical and horizontal asymptotes, multiplicities of zeros

How do you find the X-intercepts of a rational function?

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set the entire function equal to zero

• Set both numerator and denominator equal to zero

What is the X-intercept of the function 3x + 12 times X - 2?

• x = -2

• x = 1

• x = 0

• x = -4 and x = 2

How is the Y-intercept of a rational function determined?

• By substituting X with zero

• By finding the average of X-intercepts

• By setting the denominator to zero

• By setting the numerator to zero

What is the Y-intercept of the function 3x + 12 times X - 2 over X - 1 times X + 5?

• 5

• 0

• 12

• 24/5

How do you identify vertical asymptotes in a rational function?

• Set the numerator equal to zero

• Set both numerator and denominator equal to zero

• Set the denominator equal to zero and ensure it doesn't make the numerator zero

• Set the entire function equal to zero

What are the vertical asymptotes of the function 3x + 12 times X - 2 over X - 1 times X + 5?

• x = 1 and x = -5

• x = 0

• x = 2

• x = -4

How do you find horizontal asymptotes in a rational function?

• Compare the degrees of the numerator and denominator and use the ratio of leading coefficients

• Set the denominator equal to zero

• Find the average of X-intercepts

• Set the numerator equal to zero

What is the horizontal asymptote of the function 3x + 12 times X - 2 over X - 1 times X + 5?

• y = 3

• y = -3

• y = 0

• y = 1

What does a multiplicity of 1 indicate about the graph at an intercept?

• The graph has a horizontal asymptote at the intercept

• The graph touches but does not cross the intercept

• The graph crosses through the intercept

• The graph has a vertical asymptote at the intercept