Describe the domain of the function. g(x) = 1 / √(3 – 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
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 * y5)/ xy2
> Sketch the graph of the function. f (x) = x2 + 1
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x1/3)6
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (xy)6
> Use the laws of exponents to compute the numbers. (61/2)0
> Use the laws of exponents to compute the numbers. 74/3 / 71/3
> Use the laws of exponents to compute the numbers. (125 * 27)1/3
> Use the laws of exponents to compute the numbers. (8/27)2/3
> Use the laws of exponents to compute the numbers. 200.5 * 50.5
> Use the laws of exponents to compute the numbers. (21/3 * 32/3)3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = 3 / x – 6, g(x) = -2 / x - 2
> Use the laws of exponents to compute the numbers. 35/2 / 31/2
> Use the laws of exponents to compute the numbers. 104 / 54
> Describe the domain of the function. g(x) =4 / x(x + 2)
> Use the laws of exponents to compute the numbers. (94/5)5/8
> Use the laws of exponents to compute the numbers. 61/3 * 62/3
> Use the laws of exponents to compute the numbers. (31>3 * 31>6)6
> Use the laws of exponents to compute the numbers. 51/3 * 2001/3
> Compute the numbers. 1-1.2
> Compute the numbers. (.01)-1.5
> Compute the numbers. (1/8)-2/3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = 2 / x - 3, g(x) = 1 / x + 2
> Compute the numbers. 4-1/2
> Compute the numbers. (81)0.75
> Compute the numbers. 160.5
> Compute the numbers. 91.5
> Compute the numbers. (1.8)0
> Compute the numbers. (27)2/3
> Compute the numbers. (25)3/2
> Compute the numbers. 163/4
> Compute the numbers. 84/3
> Graph the following equations. y = -2x + 3
> Compute the numbers. (-5)-1
> Compute the numbers: (.01)-1
> Compute the numbers. (½)-1
> Compute the numbers. 6-1
> Describe the domain of the function. f (t) =1 / √t
> Compute the numbers. (1 / 125)1/3
> Compute the numbers. (.000001)1/3
> Compute the numbers. (27)1/3
> Compute the numbers. (16)1/2
> Compute the numbers. (.01)3
> Use intervals to describe the real numbers satisfying the inequalities. x < 3
> Compute the numbers. -42
> Compute the numbers. (100)4
> Compute the numbers. (.1)4
> Use the quadratic formula to find the zeros of the functions in Exercises 1–6. f (x) = 2x2 - 7x + 6
> 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
> Describe the domain of the function. f (x) =8x / (x - 1)(x - 2)
> 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
> 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
> 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
> In Exercises 51–54, find the points of intersection of the graphs of the functions. (Use the specified viewing window.) f (x) = 1 / x; g(x) = √(x2 – 1); [0, 4] by [-1, 3]
> Graph the following equations. y = - ½ x - 4
> In Exercises 51–54, find the points of intersection of the graphs of the functions. (Use the specified viewing window.) f (x) = 3x4 - 14x3 + 24x - 3; g(x) = 2x - 30; [-3, 5] by [-80, 30]
> In Exercises 51–54, find the points of intersection of the graphs of the functions. (Use the specified viewing window.) f (x) = -x - 2; g(x) = -4x2 + x + 1; [-2, 2] by [-5, 2]
> In Exercises 51–54, find the points of intersection of the graphs of the functions. (Use the specified viewing window.) f (x) = 2x - 1; g(x) = x2 - 2; [-4, 4] by [-6, 10]
> 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]
> In Exercises 47–50, find the zeros of the function. (Use the specified viewing window.) f (x) = √(x + 2) - x + 2; [-2, 7] by [-2, 4]
> In Exercises 47–50, find the zeros of the function. (Use the specified viewing window.) f (x) = x3 - 3x + 2; [-3, 3] [-10, 10]
> An office supply firm finds that the number of laptop computers sold in year x is given approximately by the function f (x) = 150 + 2x + x2, where x = 0 corresponds to 2015. (a) What does f (0) represent? (b) Find the number of laptops sold in 2020.
> Draw the following intervals on the number line. (4, 3π)
> In Exercises 47–50, find the zeros of the function. (Use the specified viewing window.) f (x) = x2 - x - 2; [-4, 5] [-4, 10]
> When a car is moving at x miles per hour and the driver decides to slam on the brakes, the car will travel x + (1/20) x2 feet. (The general formula is f (x) = ax + bx2, where the constant a depends on the driver’s reaction time and the constant b depends
> Graph the following equations. y = 3x + 1
> Suppose that the cable television company’s cost function in Example 4 changes to C(x) = 275 + 12x. Determine the new breakeven points.
> Solve the equations in Exercises 39–44. x2 - 8x + 16 / 1 + √x = 0
> Solve the equations in Exercises 39–44. x2 + 14x + 49 / x2 + 1 = 0
> Solve the equations in Exercises 39–44. 1 = 5 / x +6 / x2
> Solve the equations in Exercises 39–44. x + 14 / x + 4 = 5
> Solve the equations in Exercises 39–44. x + 2 / x – 6 = 3
> Solve the equations in Exercises 39–44. 21/x - x = 4
> Find the points of intersection of the pairs of curves in Exercises 31–38. y = 30x3 - 3 x2, y = 16x3 + 25x2
> The boiling point of tungsten is approximately 5933 Kelvin. (a) Find the boiling point of tungsten in degrees Celsius, given that the equation to convert x°C to Kelvin is k(x) = x + 273. (b) Find the boiling point of tungsten in degrees Fahrenheit. (Tu
> Find the points of intersection of the pairs of curves in Exercises 31–38. y = ½ x3 + x2 + 5, y = 3x2 - 12x + 5
> Graph the following equations. y = 3
