Question

question 5 of 24 step 3 of 3 consider the following rational function. \\( f(x) = \frac{-2x - 5}{x - 4} \\) step 3 of 3: identify four ordered pairs on the graph of the function. answer 2 points

Explanation:

Step1: Choose x values

Pick \( x = 0, 1, 2, 3 \) (avoid \( x = 4 \) as it makes denominator zero).

Step2: Calculate f(0)

Substitute \( x = 0 \) into \( f(x)=\frac{-2x - 5}{x - 4} \):
\( f(0)=\frac{-2(0)-5}{0 - 4}=\frac{-5}{-4}=\frac{5}{4} \), so ordered pair \( (0, \frac{5}{4}) \).

Step3: Calculate f(1)

Substitute \( x = 1 \):
\( f(1)=\frac{-2(1)-5}{1 - 4}=\frac{-7}{-3}=\frac{7}{3} \), ordered pair \( (1, \frac{7}{3}) \).

Step4: Calculate f(2)

Substitute \( x = 2 \):
\( f(2)=\frac{-2(2)-5}{2 - 4}=\frac{-9}{-2}=\frac{9}{2} \), ordered pair \( (2, \frac{9}{2}) \).

Step5: Calculate f(3)

Substitute \( x = 3 \):
\( f(3)=\frac{-2(3)-5}{3 - 4}=\frac{-11}{-1}=11 \), ordered pair \( (3, 11) \).

Answer:

Four ordered pairs are \( (0, \frac{5}{4}) \), \( (1, \frac{7}{3}) \), \( (2, \frac{9}{2}) \), \( (3, 11) \) (other valid pairs can also be used, e.g., \( x = 5 \): \( f(5)=\frac{-15}{1}=-15 \), so \( (5, -15) \), etc.).