# Standard Form and Factored Form

Please refer to the attached document for the full problem set.

20. Consider the polynomial P(x), shown in both standard form and factored form.

P(x) = (1/10)x^4 - (1/2)x^2 + (41/10)x - 3 = (1/10)(x+3)(x-1)(x-2)(x-5)

(a) Which sketch illustrates the end of behaviour of the polynomial function?

(b) State the y-intercept.

(c) State the zeros of the function.

(d) State which graph below is the graph of P(x)

21. Let f(x) = (3x -2)/(x-2).

(a) State the domain.

(b) State the vertical asymptote(s).

(c) State the horizontal asymptote.

(d) Which of the following represents the graph of f(x) = (3x-2)/(x-2)? (see attached)

22. Simplify: [(-2(a^3)(b^2))^5 * (a^-15)(b^7)]/(b^-6). Show work.

23. Points (4, -5) and (0, 1) are endpoints of the diameter of a circle.

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.

Show work.

(b) What is the center of the circle?

(c) What is the equation of the circle?

24. Find the equation for a line which passes through the points (8, -1) and (6, 3). Write the

equation in slope-intercept form. Show work.

25. A salesperson earns a base salary of $1,470 per month and a commission of 6.5% on the

amount of sales made. If the salesperson has a paycheck of $4,206.50 for one month, what was

the amount of sales for the month? Show work.

26. Let f (x) = 4x2 - 7 and g(x) = x - 5.

(a) Find the composite function (f of g)(x) and simplify. Show work.

(b) Find (f of g)(3). Show work.

27. Find the exact solutions and simplify as much as possible: 36x^2 + 5 = 24x. Show work.

28. Given the function f(x) = (1/8)(x)-2, find a formula for the inverse function. Show work.

29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P is given by P(x) = -0.002 x2 + 4.3x - 75.

(a) What is the company's profit if 600 donuts are made daily?

(b) How many donuts should be made daily in order to maximize the company's profit? Show work.

#### Solution Preview

Please refer to the attached document for full solutions.

20(a) When x<-3, it is a decreasing function, when x>5, it is an increasing function. In this case, choice C is the right one.

(b) when x=0, y=-3. So y intercept is -3.

when P(x)=0, x=-3, 1, 2 and 5. Therefore, zeros of the function is x=-3, 1, 2 and 5.

(d) based on the zeros of the function, only D is the right ...

#### Solution Summary

The solution discusses standard form and factored form.