analyze the graph of the following function solve
R(x)=x(x-16)^2 /(x+11)
solve the following inequality write solution in interval notation
x+14/x-8 less than or equal to 1
on the first on, what do you mean solve? There is no equals sign indicitaing a value.
(x+14)/(x-8)<=1
x+14<=x-8
14<=8 which is nonsense.
To analyze the graph of the function R(x) = x(x-16)^2 / (x+11), we can follow these steps:
1. Determine the x-intercepts: Set R(x) equal to zero and solve for x. In this case, the function has an x-intercept at x = 0.
2. Determine the vertical asymptotes: Set the denominator of R(x) equal to zero and solve for x. In this case, the function has a vertical asymptote at x = -11.
3. Determine the behavior near the vertical asymptote: You can analyze the behavior of the function as x approaches the vertical asymptote from both sides. In this case, as x approaches -11 from the left, R(x) approaches negative infinity, and as x approaches -11 from the right, R(x) approaches positive infinity.
4. Determine the behavior for large x-values: As x approaches positive infinity or negative infinity, R(x) will approach positive infinity.
5. Graph the function based on the information gathered from the previous steps.
For the inequality x + 14 / x - 8 ≤ 1, we can solve it as follows:
1. Multiply both sides of the inequality by (x-8) to eliminate the denominator, but remember to reverse the inequality symbol when multiplying by a negative number (since it applies when dividing by a negative number). We get x + 14 ≤ (x-8).
2. Simplify the inequality: x + 14 ≤ x - 8. By subtracting x from both sides, we get 14 ≤ -8, which is not true. Thus, there is no solution to the given inequality.
In interval notation, the solution to the inequality x + 14 / x - 8 ≤ 1 would be an empty interval, indicated by the notation ∅ or {}, which means there is no solution.