Analyzing Graphs of Rational Functions

Front

What is the domain of a rational function?

Back

The domain of a rational function is the set of all real numbers except where the denominator is zero.

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all real numbers except for any horizontal asymptotes.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the function approaches as x approaches positive or negative infinity.

Front

How do you find the x-intercepts of a rational function?

Back

Set the numerator equal to zero and solve for x.

Front

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

Back

Evaluate the function at x = 0.

Front

What is the significance of holes in the graph of a rational function?

Back

Holes occur at points where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

What does it mean if a rational function has no vertical asymptotes?

Back

It means the function does not approach infinity for any value of x, indicating the denominator does not equal zero for any real number.

Front

What is the general form of a rational function?

Back

A rational function is expressed as f(x) = P(x)/Q(x), where P and Q are polynomials.

Front

What is the behavior of a rational function near its vertical asymptotes?

Back

The function will approach positive or negative infinity as it gets close to the vertical asymptote.