Question

determine the error made when graphing the function: $y = \frac{2x - 5}{x + 1}$
step 1: y - intercept (0, - 5)
step 2: horizontal asymptote $y = 2$
step 3: vertical asymptote $x = 1$
hole: none
x - intercept $(\frac{5}{2},0)$
step 1 - y intercept should be (0, 5)
step 2 - horizontal asymptote should be $y = 0$
step 3 - vertical asymptote should be $x = - 1$
step 3 - x - intercept should be $(-\frac{5}{2},0)$

Explanation:

Step1: Find y - intercept

Set \(x = 0\) in \(y=\frac{2x - 5}{x + 1}\), then \(y=\frac{2\times0-5}{0 + 1}=-5\), so the y - intercept \((0,-5)\) is correct.

Step2: Find horizontal asymptote

Since the degree of the numerator and the denominator are the same (both degree 1), the horizontal asymptote is \(y=\frac{2}{1}=2\), so the horizontal asymptote \(y = 2\) is correct.

Step3: Find vertical asymptote

Set the denominator equal to zero: \(x+1=0\), so \(x=-1\) is the vertical asymptote. The given \(x = 1\) for the vertical asymptote is incorrect.

Answer:

Step 3 - Vertical Asymptote should be \(x=-1\)