Exploring Rational Functions: Addition and Subtraction

What are rational functions composed of?

• A polynomial function as the numerator and an exponential function as the denominator

• Two exponential functions

• A single polynomial function

• Two polynomial functions where the denominator is not zero

Why must the denominator in a rational function not be zero?

• To simplify the function's graph

• To ensure the function is defined for all real numbers

• To avoid division by zero, which is undefined

• To make the function linear

How is the domain of a rational function determined?

• By finding the derivative of the function

• By finding values that make the numerator zero

• By excluding values that make the denominator zero

• By setting the function equal to zero

What notation is used to express the domain of a rational function?

• Interval notation

• Fractional notation

• Exponential notation

• Logarithmic notation

What is the significance of the domain in a rational function?

• It indicates the slope of the function

• It specifies the maximum value of the function

• It identifies all possible x-values for the function

• It determines the range of the function

What does a vertical asymptote in a graph indicate?

• A constant value of the function

• A value that the function cannot reach

• The function's minimum value

• The function's maximum value

How is a vertical asymptote determined using limits?

• By finding where the function is undefined

• By finding where the function's derivative is zero

• By finding where the function approaches a finite value

• By finding where the function approaches positive or negative infinity

Why are limits important when studying rational functions?

• They calculate the exact value of the function at a point

• They help identify discontinuities in the function

• They determine the overall shape of the graph

• They simplify the function for easier analysis

What does it mean if a function has a horizontal asymptote at y=0?

• The function is undefined at y=0

• The function has no vertical asymptotes

• The function approaches zero as x approaches infinity

• The function crosses the y-axis at zero

How can you determine the horizontal asymptotes of a function?

• By plotting the function on a graph

• By setting the numerator equal to zero

• By evaluating the limits as x approaches positive and negative infinity

• By finding the function's derivatives