Vocabulary & Basics
What is a rational function?
A function written as a ratio of two polynomials
What value is excluded from the domain of f(x)=1/x-2
x=2
What creates a vertical asymptote?
A zero in the denominator that doesn’t cancel
How do you find x-intercepts?
Set numerator = 0
What is the first step when graphing a rational function?
Find domain restrictions
What causes a function to be undefined?
A zero in the denominator
Find the domain of 2/x+5
All real numbers except {-5}
How do you find horizontal asymptotes?
Compare degrees of numerator and denominator
How do you find the y-intercept?
Evaluate f(0), if defined
Why do we sketch asymptotes before plotting points?
They guide the shape of the graph
What is an asymptote?
A line the graph approaches but does not cross
How do you find domain restrictions?
Set the denominator ≠ 0
What happens when degrees are equal?
HA = ratio of leading coefficients
Can a rational function have no x-intercept?
Yes
How does a hole change the graph?
It creates a missing point
What is a vertical asymptote?
A vertical line where the function is undefined
Does a hole affect the domain? Explain.
Yes, the x-value is excluded
What if numerator degree < denominator degree?
HA is y = 0
Explain why vertical asymptotes are not intercepts
The function is undefined there
Describe how the graph behaves near a vertical asymptote
Approaches ±∞
What is a hole in a graph?
A removable discontinuity caused by a common factor
Identify domain restrictions from a factored rational function
Based on cancelled and non-cancelled factors
When do we get a slant asymptote?
Numerator degree is one more than denominator
Determine intercepts from a given rational function
Correct x and y values
Explain the complete graphing process step-by-step
Domain → Asymptotes → Intercepts → Shape