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)
> Relate to the function whose graph is sketched in Fig. 12. Find f (2) and f (-1). Y1= +6) X=2.01 Y=2.000833 [1.2899, 2.5399] by [1.3679, 2.6179] When x = 2, y=2. Find a second point on the line using value: x = 2.01, y= 2.000833 2.000833 – 2 m = =
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (-8y9)2/3
> 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. Y1=CX-1/0*+1 X=1.01 Y=.00497512 [.93251, 1.08876] by [-.
> 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. M1=2x2-3%+2 X=.05 Iy=i.855
> Decide which curves are graphs of functions. y = f(x) 3 3 3 + h Figure 17 Geometric representation of values.
> Consider a circle of radius r. Write an expression for the area. Write an equation expressing the fact that the circumference is 15 centimeters.
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (25xy)3/2 / x2y
> Consider the rectangle in Exercise 1. Write an expression for the area. Write an equation expressing the fact that the perimeter is 30 centimeters. y = x³| (x, y) Slope is 3a Figure 15 Slope of tangent line to y = x³.
> 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. y = -x - y = x² a
> Assign variables to the dimensions of the geometric object. y = x2 y = 2x – 1 a
> 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 + 2) + g(x + 2)
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (16x8)-3/4
> 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.
> 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)
> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. f (g(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
> Convert the numbers from graphing calculator form to standard form (that is, without E). 1.35E13
> Refer to the cost function in Fig. 18. Translate the task “find C(400)” into a task involving the graph. Vx for 0<x < 2 f (x) = - |1+x for 2 <x<5 f(1) = Vĩ = 1 f(2) = 1+2 = 3 f (3) = 1+3 = 4
> 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
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 1 / yx-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.
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. h (f (t))
> Draw the following intervals on the number line. (4, 3π)
> 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?
> Refer to the cost function in Fig. 18. Translate the task “solve C(x) = 3500 for x” into a task involving the graph of the function. C D B E A Figure 12
> If the cylinder in Exercise 6 has a volume of 54p cubic inches, find the surface area of the cylinder. Cylinder in Exercise 6: C D B E A Figure 12
> 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%
> Describe the domain of the function. f (x) =8x / (x - 1)(x - 2)
> Decide which curves are graphs of functions. 8 7 6 3 2 1 2 3 4 5 6 7 8 4) 1.
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 2x / √x
> 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%
> In Exercises 47–50, find the zeros of the function. (Use the specified viewing window.) f (x) = x2 - x - 2; [-4, 5] [-4, 10]
> 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%
> 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]
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) + g(x)
> A catering company estimates that, if it has x customers in a typical week, its expenses will be approximately C(x) = 550x + 6500 dollars, and its revenue will be approximately R(x) = 1200x dollars. (a) How much profit will the company earn in 1 week whe
> 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
> Sketch the graph of the function. f (x) = √(x + 1)
> Evaluate f (4). f (x) = x-1/2
> Evaluate f (4). f (x) = x3/2
> Decide which curves are graphs of functions. x = degrees Fahrenheit, y = degrees Celsius, so the points (32, 0) and (212, 100) lie on the line. 100 – 0 100 5 212 – 32 180 9 Now find b: 160 y = mx + b= 32 ㅎ = (0)+b=b: 9 5 160 Thus, y =x+32. y=-(98.6)
> 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
> Draw the following intervals on the number line. [ -2, √2)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. g(x) - h(x - 3)
> 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
> 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
> 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. x-1/4 + 6x1/4 = x-1/4( )
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. [ f (x)]3g(x)
> Graph the following equations. y = 3x + 1
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. 2x2/3 - x-1/3 = x-1/3 ( )
> 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
> Refer to the cost and revenue functions in Fig. 17. The cost of producing x units of goods is C(x) dollars and the revenue from selling x units of goods is R(x) dollars. At what level of production is the cost $1400? 1 x+ 2y = 0= y = --x= m = 2 1 2
> 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
> The expressions in Exercises 83–88 may be factored as shown. Find the missing factors. √x – 1/√x = 1/√x ( )
> Solve the equations in Exercises 39–44. 1 = 5 / x +6 / x2
> 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
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) + h(x)
> 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
> Solve the equations in Exercises 39–44. x + 14 / x + 4 = 5
> 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
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. g(x) - h(x)
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. (x4 * y5)/ xy2
