The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. x-1/4 + 6x1/4 = x-1/4( )
> 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) / g(x)
> Consider the rectangular box in Exercise 3, and suppose that it has no top. Write an expression for the volume. Write an equation expressing the fact that the surface area is 65 square inches. Rectangle with height = 3 - width
> Consider the Norman window of Exercise 2. Write an expression for the perimeter. Write an equation expressing the fact that the area is 2.5 square meters. Norman window: Rectangle topped with a semicircle
> Decide which curves are graphs of functions. -x
> Consider a circle of radius r. Write an expression for the area. Write an equation expressing the fact that the circumference is 15 centimeters.
> Consider the rectangle in Exercise 1. Write an expression for the area. Write an equation expressing the fact that the perimeter is 30 centimeters. Rectangle with height = 3- width
> Consider the rectangle in Exercise 1. Write an expression for the perimeter. If the area is 25 square feet, write this fact as an equation. Rectangle with height = 3- width
> Assign variables to the dimensions of the geometric object. Cylinder with height = diameter
> Assign variables to the dimensions of the geometric object. Сyinder
> Compute the numbers. 025
> Compute the numbers. 1100
> 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. g(x)h(x)
> Compute the numbers. (-2)3
> Compute the numbers. 33
> Convert the numbers from graphing calculator form to standard form (that is, without E). 8.23E-6
> Decide which curves are graphs of functions.
> Convert the numbers from graphing calculator form to standard form (that is, without E). 1.35E13
> Convert the numbers from graphing calculator form to standard form (that is, without E). 8.103E-4
> Convert the numbers from graphing calculator form to standard form (that is, without E). 5E-5
> Velocity When a car’s brakes are slammed on at a speed of x miles per hour, the stopping distance is 1 20x2 feet. Show that when the speed is doubled the stopping distance increases fourfold.
> Semiannual Compound Assume that a $1000 investment earns interest compounded semiannually. Express the value of the investment after 2 years as a polynomial in the annual rate of interest r.
> Assume that a $500 investment earns interest compounded quarterly. Express the value of the investment after 1 year as a polynomial in the annual rate of interest r.
> Use intervals to describe the real numbers satisfying the inequalities. x ≥ 12
> Assume that a couple invests $4000 each year for 4 years in an investment that earns 8% compounded annually. What will the value of the investment be 8 years after the first amount is invested?
> Assume that a couple invests $1000 upon the birth of their daughter. Assume that the investment earns 6.8% compounded annually. What will the investment be worth on the daughter’s 18th birthday?
> Calculate the compound amount from the given data. principal = $1500, compounded daily, 3 years, annual rate = 6%
> Calculate the compound amount from the given data. principal = $1500, compounded daily,1 year, annual rate = 6%
> Decide which curves are graphs of functions.
> Calculate the compound amount from the given data. principal = $500, compounded monthly,1 year, annual rate = 4.5%
> Calculate the compound amount from the given data. principal = $100, compounded monthly, 10 years, annual rate = 5%
> Calculate the compound amount from the given data. principal = $20,000, compounded quarterly, 3 years, annual rate = 12%
> Calculate the compound amount from the given data. principal = $50,000, compounded quarterly, 10 years, annual rate = 9.5%
> Calculate the compound amount from the given data. principal = $700, compounded annually, 8 years, annual rate = 8%
> 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)g(x)
> Calculate the compound amount from the given data. principal = $500, compounded annually, 6 years, annual rate = 6%
> Evaluate f (4). f (x) = x0
> Evaluate f (4). f (x) = x-5/2
> Evaluate f (4). f (x) = x-1/2
> Evaluate f (4). f (x) = x3/2
> Decide which curves are graphs of functions. -x
> Draw the following intervals on the number line. [ -2, √2)
> Evaluate f (4). f (x) = x1/2
> Evaluate f (4). f (x) = x-1
> Evaluate f (4). f (x) = x3
> 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 (t) - h(t)
> Evaluate f (4). f (x) = x2
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a/√b = √ (a/b).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. Explain why √a * √b = √(ab).
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √ (x/y) - √ (y/x) = √xy ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. 2x2/3 - x-1/3 = x-1/3 ( )
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √x – 1/√x = 1/√x ( )
> Decide which curves are graphs of functions.
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (f (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) - g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g (f (x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. 3√ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. √ (f (x)/ g(x))
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)g(x)]3
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)]3g(x)
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g(x) / f (x)
> Sketch the graph of the function. f (x) = 1 / f(x) = x + 1
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. f (x) / g(x)
> 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
> Use intervals to describe the real numbers satisfying the inequalities. x ≥ -1 and x < 8
> 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. Your answer should not involve parentheses or negative exponents. (-32y-5)3/5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-27x5)2/3 / x3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (25xy)3/2 / x2y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √x (1/4x)5/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-8y9)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (16x8)-3/4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1 / yx-5
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 2x / √x
> Sketch the graph of the function. f (x) = √(x + 1)
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x + 5 / x – 10, g(x) = x / x + 10
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x2 / x5y
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (3x2 / 2y)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x)3/2 * (x)2/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-3x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-4 / x3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x3 / y-2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -x3y / -xy
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. -3x / 15x4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (2x)4
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) =-x / x + 3, g(x) = x / x + 5
> Sketch the graph of the function. f (x) = 2x2 - 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-3 * x7
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x5 * (y2 / x)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √(1 + x) * (1 + x)3/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3y5)4
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x/y)-2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 / y2)3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x3 * y6)1/3
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. x-1/2
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1/x-3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = x / x - 8, g(x) =-x / x - 4
