Show all steps. Simplify your answers.
Problem 1. Solve the inequality. Express the solution both on the number line and in interval notation. Use
exact forms (such as fractions) instead of decimal approximations: 2x-3
≤0
5x411
Problem 2. Solve the inequality algebraically and write the solution as an interval 13-2x ≥ 5
Problem 3. Find the x - and y-intercepts, the domain, the vertical and horizontal asymptotes, and then
sketch a complete graph of the function f(x) =
3x-6
1-x
Problem 4. Let u = ln(x) and v= In(y), where x, y > 0. Write the following expression in terms of u and v.
In (ys √x³)
Problem 5. Find the domain, asymptotes, and x-intercept of the function, and then sketch its graph:
f(x) = log(4x)
Problem 6. Find the inverse of the function y=X+2
Problem 7. Find the sum of the first 50 terms of the arithmetic sequence 3, 11, 19, 27, 35,
f(x+h)-f(x) (assume h = 0) for f(x) = 3x² + 2x + 5
h
Problem 8. Find the difference quotient
3