Question

Which graph represents the function?

f(x)=1x−1−2


Responses

Graph of a rational function. The horizontal axis ranges from negative 5 to 5 in increments of 1. The vertical axis ranges from negative 5 to 5 in increments of 1. The function has two branches. The left branch passes through begin ordered pair negative 2 comma 1 end ordered pair and approaches the line y equals 2 and the line x equals negative 1. The right branch passes through begin ordered pair 0 comma 3 end ordered pair and approaches the line y equal 2 and the line x equals negative 1.
Image with description Graph of a rational function. The horizontal axis ranges from negative 5 to 5 in increments of 1. The vertical axis ranges from negative 5 to 5 in increments of 1. The function has two branches. The left branch passes through begin ordered pair negative 2 comma 1 end ordered pair and approaches the line y equals 2 and the line x equals negative 1. The right branch passes through begin ordered pair 0 comma 3 end ordered pair and approaches the line y equal 2 and the line x equals negative 1.
Graph of a rational function. The horizontal axis ranges from negative 5 to 5 in increments of 1. The vertical axis ranges from negative 5 to 5 in increments of 1. The function has two branches. The left branch passes through begin ordered pair 0 comma 1 end ordered pair and approaches the line y equals 2 and the line x equals 1. The right branch passes through begin ordered pair 2 comma 3 end ordered pair and approaches the line y equals 2 and the line x equals 1.
Image with description Graph of a rational function. The horizontal axis ranges from negative 5 to 5 in increments of 1. The vertical axis ranges from negative 5 to 5 in increments of 1. The function has two branches. The left branch passes through begin ordered pair 0 comma 1 end ordered pair and approaches the line y equals 2 and the line x equals 1. The right branch passes through begin ordered pair 2 comma 3 end ordered pair and approaches the line y equals 2 and the line x equals 1.
Graph of a rational function. The horizontal axis ranges from negative 5 to 5 in increments of 1. The vertical axis ranges from negative 5 to 5 in increments of 1. The function has two branches. The left branch passes through begin ordered pair 0 comma negative 3 end ordered pair and approaches the line y equals negative 2 and the line x equals 1. The right branch passes through begin ordered pair 2 comma negative 1 end ordered pair and approaches the line y equals negative 2 and the line x equals 1.
Image with description Graph of a rational function. The horizontal axis ranges from negative 5 to 5 in increments of 1. The vertical axis ranges from negative 5 to 5 in increments of 1. The function has two branches. The left branch passes through begin ordered pair 0 comma negative 3 end ordered pair and approaches the line y equals negative 2 and the line x equals 1. The right branch passes through begin ordered pair 2 comma negative 1 end ordered pair and approaches the line y equals negative 2 and the line x equals 1.
Graph of a rational function. The horizontal axis ranges from negative 5 to 5 in increments of 1. The vertical axis ranges from negative 5 to 5 in increments of 1. The function has two branches. The left branch passes through begin ordered pair negative 2 comma negative 3 end ordered pair and approaches the line y equals negative 2 and the line x equals negative 1. The right branch passes through begin ordered pair 0 comma negative 1 end ordered pair and approaches the line y equals negative 2 and the line x equals negative 1.

Answer 1

f(x) = 1/(x−1) − 2 has vertical asymptote x = 1 and horizontal asymptote y = −2. Also f(0) = −3 and f(2) = −1.

So the correct graph is the one that approaches x = 1 and y = −2 and has the left branch through (0, −3) and the right branch through (2, −1).