Exploring Slant Asymptotes in Rational Functions

What is a vertical asymptote?

• A line that the graph approaches but never touches, occurring where the denominator equals zero.

• A line that the graph crosses at y equals zero.

• A line that the graph crosses at x equals zero.

• A line that the graph approaches as x approaches infinity.

When does a horizontal asymptote occur at y equals zero?

• When the degree of the numerator is larger than the degree of the denominator.

• When the degree of the numerator is equal to the degree of the denominator.

• When the numerator equals zero.

• When the degree of the denominator is larger than the degree of the numerator.

Under what condition does a slant asymptote occur?

• When the degree of the numerator is one greater than the degree of the denominator.

• When the numerator equals zero.

• When the degree of the denominator is larger than the degree of the numerator.

• When the degree of the numerator is equal to the degree of the denominator.

What method can be used to find slant asymptotes?

• Completing the square

• Factoring

• Long division

• Synthetic division

What is the slant asymptote of the function given in the video?

• y = x + 4

• y = x + 3

• y = x - 3

• y = x - 4

How do you find the y-intercept of a rational function?

• Set y to zero and solve for x.

• Find where the denominator equals zero.

• Set x to zero and solve for y.

• Find where the numerator equals zero.

What are the x-intercepts of the function in the video?

• x = -3 and x = 2

• x = 3 and x = -2

• x = -3 and x = -2

• x = 3 and x = 2

What happens to the graph on the right side of the vertical asymptote?

• It approaches the x-axis.

• It approaches the y-axis.

• It approaches the slant asymptote from above.

• It approaches the slant asymptote from below.

What is the value of the function at x equals 4?

• 14

• 10

• 12

• 16

What additional information is needed to make a good graph?

• The leading coefficient

• The degree of the numerator

• The degree of the denominator

• Symmetry properties