2. Vocabulary
1. Rational Function: A function that is the ratio of two polynomials.
2. Asymptote: A line that a graph approaches but never touches.
3. Vertical Asymptote: A vertical line where the function is
undefined, often where the denominator equals zero.
4. Horizontal Asymptote: A horizontal line the graph approaches as
x goes to infinity or negative infinity.
5. Intercept: The points where the graph crosses the x-axis or y-axis.
3. Examples with Key to Correction
1. Vertical asymptote of f(x) = 1 / (x - 3): x = 3
2. Horizontal asymptote of f(x) = (2x² + 3) / (x² - 1): y = 2
3. Intercepts of f(x) = (x - 2) / (x + 1): x-intercept: x = 2, y-
intercept: y = -2
4. Graph of f(x) = 1 / x: Hyperbola with asymptotes at x = 0 and y
= 0
5. Asymptotes of f(x) = (x + 4) / (x - 1): Vertical asymptote: x = 1,
Horizontal asymptote: y = 1
4. Multiple-Choice Quiz (1-5)
1. What is a rational function?
A) Sum of polynomials B) Ratio of polynomials C) Product of polynomials D) Difference of polynomials
2. Which describes an asymptote?
A) Intersection point B) Maximum value C) Line the graph approaches but never touches D) Y-intercept
3. Vertical asymptote of f(x) = 1/(x + 2):
A) x = -2 B) x = 2 C) y = 2 D) y = -2
4. Horizontal asymptote of f(x) = (3x)/(x + 1):
A) y = 3 B) y = 1 C) y = 0 D) y = x
5. x-intercept of f(x) = (x - 4)/(x + 3):
A) x = -4 B) x = 4 C) x = -3 D) x = 3
5. Multiple-Choice Quiz (6-10)
6. Asymptotes help to:
A) Determine intercepts B) Identify maximum values C) Understand graph behavior D) Solve equations
7. What happens to f(x) = 1/x at x = 0?
A) Crosses axis B) Vertical asymptote C) Maximum D) Nothing
8. If numerator and denominator degrees are equal, horizontal asymptote is:
A) 0 B) Ratio of leading coefficients C) Infinity D) Undefined
9. Vertical asymptote of f(x) = (x + 1)/(x - 5):
A) x = 5 B) x = -1 C) y = 1 D) y = -5
10. Y-intercept is found by:
A) Setting x = 0 B) Setting y = 0 C) Finding asymptotes D) Solving for maximum
6. Answer Key
1 - B
2 - C
3 - A
4 - A
5 - B
6 - C
7 - B
8 - B
9 - A
10 - A
