Question

consider the following rational function.
$f(x) = \frac{x^2 + 10}{x^3 - 64}$
step 3 of 3: identify four ordered pairs on the graph of the function.
answer 2 points

Explanation:

Step1: Choose x=0

Substitute \( x = 0 \) into \( f(x)=\frac{x^{2}+10}{x^{3}-64} \).
\( f(0)=\frac{0^{2}+10}{0^{3}-64}=\frac{10}{-64}=-\frac{5}{32} \).
Ordered pair: \( (0, -\frac{5}{32}) \).

Step2: Choose x=1

Substitute \( x = 1 \) into \( f(x) \).
\( f(1)=\frac{1^{2}+10}{1^{3}-64}=\frac{11}{-63}=-\frac{11}{63} \).
Ordered pair: \( (1, -\frac{11}{63}) \).

Step3: Choose x=2

Substitute \( x = 2 \) into \( f(x) \).
\( f(2)=\frac{2^{2}+10}{2^{3}-64}=\frac{4 + 10}{8 - 64}=\frac{14}{-56}=-\frac{1}{4} \).
Ordered pair: \( (2, -\frac{1}{4}) \).

Step4: Choose x=5

Substitute \( x = 5 \) into \( f(x) \).
\( f(5)=\frac{5^{2}+10}{5^{3}-64}=\frac{25 + 10}{125 - 64}=\frac{35}{61} \).
Ordered pair: \( (5, \frac{35}{61}) \).

Answer:

\( (0, -\frac{5}{32}) \), \( (1, -\frac{11}{63}) \), \( (2, -\frac{1}{4}) \), \( (5, \frac{35}{61}) \) (Other valid pairs are also acceptable, e.g., using different x - values as long as \( x
eq4 \) to avoid division by zero).