MATH 115 MIDTERM NAME: 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) 2 g(x) or the inequality f(x) s 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) =x - 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) = 3x- - 3 x2 - 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. 5. (10 pts) Solve the equation. Check all proposed solutions. V19 - 3x = x -5 6. (10 pts) Solve for x. Check all points x- 1 x+1- 7. (30 pts 10 each) Let f (x) = ex-2 +3. Answers can be stated without additional work/explanation. (a) Which describes how the graph of f can be obtained from the graph of y = e" ? Choice: A. Shift the graph of y = e up by 1 unit. B. Shift the graph of y = e" to the left by 2 units and up by 3 units. C. Shift the graph of y = e" to the right by 2 units and up by 3 units. D. Shrink the graph of y = e" horizontally by a factor of 2 and shift up by 3 units. (b) What is the y-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth). (c) Which is the graph of f? GRAPH A GRAPH B GRAPH C 10- 10 10