Graph the function. Be sure to label all the asymptotes. List the domain and the x- and y-interc

step 1 We have given f of x is equal to x minus 1 divided by x plus 2. We see that at x equal to minus

Graph the function. Be sure to label all the asymptotes....

Key Concepts

Rational Functions

Rational functions are expressions represented as the ratio of two polynomials. They are important in understanding behaviors such as asymptotic behavior, holes, and intercepts, and are commonly analyzed by considering their numerator and denominator separately.

Vertical Asymptote

A vertical asymptote occurs where a rational function becomes undefined due to division by zero, and the function's value tends to infinity or negative infinity as it approaches that x-value. It is determined by setting the denominator equal to zero and ensuring the numerator does not also become zero at that point.

Horizontal Asymptote

A horizontal asymptote describes the end behavior of a function as x approaches positive or negative infinity. For rational functions, it is often found by comparing the degrees of the numerator and denominator; if they are equal, the horizontal asymptote is the ratio of the leading coefficients.

Intercepts

Intercepts are the points where the graph of a function crosses the axes. The x-intercept(s) are found by setting the function equal to zero (usually by solving the numerator), while the y-intercept is found by evaluating the function at x = 0.

Domain

The domain of a function includes all possible x-values for which the function is defined. For rational functions, any x-value that makes the denominator zero must be excluded from the domain.

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