Suppose that $7000 is deposited in a savings account that pays 9% per annum, compounded biannually, for t years. (a) Express the account balance A(t) as a function of t, the number of years that the principal has been in the account. (b) Calculate the account balance at the end of 10 years and at the end of 20 years.
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (g(x))
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x + 1) g(x + 1)
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x)g(x)
> Use intervals to describe the real numbers satisfying the inequalities. x < 3
> Compute the numbers. -42
> Find an equation of the given line. Horizontal through (√7, 2)
> Find an equation of the given line. Slope is -2; x-intercept is -2
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> Find an equation of the given line. Slope is 2; x-intercept is -3
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. f (h(x))
> Evaluate each of the functions in Exercises 37–42 at the given value of x. f (x) = |x|, x = -2/3
> Find an equation of the given line. x-intercept is -π; y-intercept is 1
> Find an equation of the given line. x-intercept is 1; y-intercept is -3
> Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial. f (x) = 3x3 + 52x2 - 12x - 12
> Relate to the function whose graph is sketched in Fig. 12. Find f (0) and f (7). 4 -3 -2 -1 1 2 3 4 4,
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. 3√ (f (x)g(x))
> Find an equation of the given line. Horizontal through (2, 9)
> Find an equation of the given line. (- 1/2, - 1/7) and (2/3, 1) on line
> Compute the numbers. (100)4
> Find an equation of the given line. (0, 0) and (1, 0) on line
> Find an equation of the given line. (1/2, 1) and (1, 4) on line
> Find an equation of the given line. (5/7, 5) and (- 5/7 , -4) on line
> Find an equation of the given line. Slope is 7/3; (1/4, - 2/5) on line
> Find an equation of the given line. Slope is 1/2 ; (2, 1) on line
> If f (x) = x2 - 3x, find f (0), f (5), f (3), and f (-7).
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> In Exercises 47–50, find the zeros of the function. (Use the specified viewing window.) f (x) = x / (x + 2) - x2 + 1; [-1.5, 2] by [-2, 3]
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. g (h(t))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)g(x))
> Find an equation of the given line. Slope is 2; (1, -2) on line
> Find an equation of the given line. Slope is -1; (7, 1) on line
> Find the slopes and y-intercepts of the following lines. 4x + 9y = -1
> Compute the numbers. (.1)4
> Find the slopes and y-intercepts of the following lines. y = x/7 - 5
> Find the slopes and y-intercepts of the following lines. y = 6
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(x) / f (x)
> Determine the domains of the following functions. f (x) = 1 / x(x + 3)
> Let f (x) = [1/(x + 1)] - x2. Evaluate f (a + 1).
> Graph the following equations. y = 3
> Let f (x) = x2 - 2. Evaluate f (a - 2).
> Let f (x) = 2x + 3x2. Evaluate f (0), f (- 1/4), and f (1/√2).
> Suppose that the cable television company’s cost function in Example 4 changes to C(x) = 275 + 12x. Determine the new breakeven points.
> Let f (x) = x3 +1 /x. Evaluate f (1), f (3), f (-1), f (- 12), and f (√2).
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. g (f (x))
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> Suppose that $7000 is deposited in a savings account that pays a rate of interest r per annum, compounded annually, for 20 years. (a) Express the account balance A(r) as a function of r. (b) Calculate the account balance for r = .07 and r = .12.
> Solve the equations in Exercises 39–44. x2 + 14x + 49 / x2 + 1 = 0
> Use the quadratic formula to find the zeros of the functions in Exercises 1–6. f (x) = 2x2 - 7x + 6
> Suppose that $15,000 is deposited in a savings account that pays a rate of interest r per annum, compounded annually, for 10 years. (a) Express the account balance A(r) as a function of r. (b) Calculate the account balance for r = 0.04 and r = 0.06
> Refer to the function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16. Interpret the fact that the point (3, 162) is on the graph of the function. 1 lim lim
> Suppose that $15,000 is deposited in a savings account that pays 4% per annum, compounded monthly, for t years. (a) Express the account balance A(t) as a function of t, the number of years that the principal has been in the account. (b) Calculate the acc
> Use the laws of exponents to simplify the algebraic expressions. 3√x (8x2/3)
> Use the laws of exponents to simplify the algebraic expressions. x3/2/ √x
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)/ g(x))
> Use the laws of exponents to simplify the algebraic expressions. xy3 / x-5y6
> Use the laws of exponents to simplify the algebraic expressions. (√(x + 1))4
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x)h(x)
> The revenue R(x) (in thousands of dollars) that a company receives from the sale of x thousand units is given by R(x) = 5x - x2. The sales level x is in turn a function f (d) of the number d of dollars spent on advertising, where Express the revenue as
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. h(g(x))
> The population of a city is estimated to be 750 + 25t + .1t2 thousand people t years from the present. Ecologists estimate that the average level of carbon monoxide in the air above the city will be 1 + .4x ppm (parts per million) when the population is
> Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial. f (x) = 2x5 - 24x4 - 24x + 2
> Refer to the function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16. For what value(s) of r is the cost 330 cents? Vx2 – 5x – 36 lim x-5 8- 3х 1/2 lim x? -
> Find the points of intersection of the pairs of curves in Exercises 31–38. y = ½ x3 + x2 + 5, y = 3x2 - 12x + 5
> Relate to the function whose graph is sketched in Fig. 12. For what values of x is f (x) ≤ 0? lim (x + Vx - 6)(x² - 2x +1) 6) (x² – 2x + 1) = lim (x + Vx - 6)(x – 1)? x→7 lim x+ lim Vr – 6 | lim x – lim 1 x→7 x→7 = (7+1)(7 – 1)²
> Find the points of intersection of the curves y = -x2 + x + 1 and y = x - 5.
> Find the points of intersection of the curves y = 5x2 - 3x – 2 and y = 2x - 1.
> Find the zeros of the quadratic function y = -2x2 - x + 2.
> Find the zeros of the quadratic function y = 5x2 - 3x - 2.
> Factor the polynomials. x5 - x4 - 2x3
> Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial. f (x) = x4 - 200x3 - 100x2
> Sketch the graph of the function. f (x) = 1 / f(x) = x + 1
> Factor the polynomials. 18 + 3x - x2
> An average sale at a small florist shop is $21, so the shop’s weekly revenue function is R(x) = 21x, where x is the number of sales in 1 week. The corresponding weekly cost is C(x) = 9x + 800 dollars. (a) What is the florist shop’s weekly profit function
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> Draw the following intervals on the number line. [ -1, 4]
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. f (g(x))
> Factor the polynomials. 3x2 - 3x - 60
> Factor the polynomials. 5x3 + 15x2 - 20x
> Is the point (1, -2) on the graph of the function k(x) = x2 + (2/x)?
> Is the point (1/2, - 3/5) on the graph of the function h(x) = (x2 - 1)/(x2 + 1)?
> Relate to the function whose graph is sketched in Fig. 12. For what values of x does f (x) = 0? nDeriv(2"X,X,0) 6931472361
> Draw the following intervals on the number line. [1, 3/2]
> Determine the domains of the following functions. f (x) = 1 /√(3x)
> Determine the domains of the following functions. f (x) = √(x2 + 1)
> Simplify (100)3/2 and (.001)1/3.
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x) / g(x)
> A cellular telephone company estimates that, if it has x thousand subscribers, its monthly profit is P(x) thousand dollars, where P(x) = 12x - 200. (a) How many subscribers are needed for a monthly profit of 160 thousand dollars? (b) How many new subscri
> Find a good window setting for the graph of the function. The graph should show all the zeros of the polynomial. f (x) = x3 - 22x2 + 17x + 19
> Determine the domains of the following functions. f (x) = √(x – 1)
> What is the difference between an open interval and a closed interval from a to b?
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. h(1/x2)
> What are the four types of inequalities, and what do they each mean?
> Explain the relationships and differences among real numbers, rational numbers, and irrational numbers.
> Explain how to find f (a) geometrically from the graph of y = f (x).
> Explain how to solve f (x) = b geometrically from the graph of y = f (x).
> Simplify (81)3/4, 85/3, and (.25)-1.
> In the formula A = P(1 + i)n, what do A, P, i, and n represent?
> State the six laws of exponents.
> A frozen yogurt stand makes a profit of P(x) = .40x – 80 dollars when selling x scoops of yogurt per day. (a) Find the breakeven sales level, that is, the level at which P(x) = 0. (b) What sales level generates a daily profit of $30? (c) How many more s
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 6 / x – 6, g(x) = x – 6 / x + 6
