Mathematics Quiz on Functions and Asymptotes

What is a discontinuity in a function?

• A point where the function is continuous

• A circumstance that causes a gap in the domain or range of a function

• A point where the function is differentiable

• A point where the function is integrable

Where is a vertical asymptote located in a rational function?

• In the numerator

• In the denominator

• In the constant term

• In the exponent

What happens when there is a common factor in the numerator and denominator of a rational function?

• The common factor is multiplied

• The common factor is added

• The common factor is canceled out in the simplified/final expression

• The common factor is squared

Graph of the function f(x) = x^2 + 4x - 12

• Graph A: A parabola opening upwards with vertex at (-2, -16)

• Graph B: A parabola opening downwards with vertex at (0, -12)

• Graph C: A parabola opening upwards with vertex at (-2, -12)

• Graph D: A parabola opening upwards with vertex at (2, 12)

What is a vertical asymptote in a rational function?

• A point where the graph crosses the x-axis

• A discontinuity located in the denominator of a rational function

• A point where the graph crosses the y-axis

• A horizontal line that the graph approaches

In Case #1 of horizontal asymptotes, when the degree of the numerator is smaller than the degree in the denominator, where is the horizontal asymptote?

• At y = 0

• At x = 0

• At y = 1

• At x = 1

In Case #2 of horizontal asymptotes, when the numerator and denominator have an equal degree, what do you use to find the horizontal asymptote?

• The sum of the coefficients

• The difference of the coefficients

• The ratio of the leading coefficients

• The product of the coefficients

In Case #3 of horizontal asymptotes, when the degree in the numerator is one degree higher than in the denominator, what type of asymptote do you have?

• Vertical asymptote

• Horizontal asymptote

• Oblique asymptote

• No asymptote

What is a "hole" in a rational function?

• A point where the graph intersects the x-axis

• A point where the graph intersects the y-axis

• A point where a factor in the numerator and denominator cancels out

• A point where the graph is undefined

Where is a hole located in a rational function?

• At the y-intercept

• At the x-intercept

• At the solution of the factor that cancels out

• At the origin