With work shown

SHOW WORK FOR ALL PROBLEMS. 1. (5 pts) Convert to a logarithmic equation: 3* = 243. 2. (15 pts 5 each part) Laura is a salesperson who must decide between two monthly income options. Option A: Salary of $1030 per month, plus 12% of monthly sales (in dollars) or Option B: Salary of $1882 per month, plus 8% of monthly sales (in dollars) (a) State a linear function f(x) that represents the Option A total income, given monthly sales of x dollars. (b) State a linear function g(x) that represents the Option B total income, given monthly sales of x dollars. (c) Laura wants to determine the following: For what amount of monthly sales is Option A the better choice rather than Option B? To answer the question, should you solve the inequality f(x) > g(x) or the inequality f(x) = g(x) ? Write the appropriate inequality, show how to solve it, and state your answer to the question in a| sentence. 3. (10 pts 5 each) Let f(x) =x3 - 8x + 9 and g(x) = 3x + 5 (a) Find the composite function (f o g ) (x) and simplify the results. Show work. (b) Find (fog)(-2) . Show work. 4. (20 pts 5 each) Let f (x) = - 4 (no explanations required) (a) State the y-intercept. (b) State the x-intercept(s). (c) State the vertical asymptote(s). (d) State the horizontal asymptote