Section 3.6

문제 73

In Exercises 73–74, use the graph of the rational function to solve each inequality.

1/4(x + 2) ≤ - 3/4(x - 2)

문제 74

In Exercises 73–74, use the graph of the rational function to solve each inequality.

1/4(x + 2) > - 3/4(x - 2)

문제 86

Solve each inequality in Exercises 86–91 using a graphing utility. x² + 3x - 10 > 0

문제 87

Solve each inequality in Exercises 86–91 using a graphing utility. 2x² + 5x - 3 ≤ 0

문제 88

Solve each inequality in Exercises 86–91 using a graphing utility. x³ + x² - 4x - 4 > 0

문제 89

Solve each inequality in Exercises 86–91 using a graphing utility. (x - 4)/(x - 1) ≤ 0

문제 91

Solve each inequality in Exercises 86–91 using a graphing utility. 1/(x + 1) ≤ 2/(x + 4)

Section 3.7

문제 1

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies directly as x. y = 65 when x = 5. Find y when x = 12.

문제 3

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies inversely as x. y = 12 when x = 5. Find y when x = 2.

문제 5

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies directly as x and inversely as the square of z. y = 20 when x = 50 and z = 5. Find y when x = 3 and z = 6.

문제 7

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as x and z. y = 25 when x = 2 and z = 5. Find y when x = 8 and z = 12.

문제 9

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.

문제 11

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z.

문제 13

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube of z and inversely as y.

문제 14

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube root of z and inversely as y.

문제 15

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square root of w.

문제 16

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square of w.

문제 17

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as z and the sum of y and w.

문제 18

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as z and the difference between y and w.

문제 19

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the difference between y and w.

문제 20

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the sum of y and w.

문제 45

Describe in words the variation shown by the given equation. $z = \frac{k\sqrt{x}}{y^2}$

문제 59

Solve: $\sqrt{x} + \sqrt{x + 5} = 5$

문제 60

Find the inverse of f(x) = x³ + 2

Review Exercises

문제 1

In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range.

$f (x) = - (x + 1)^{2} + 4$

문제 3

In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $f (x) = - x^{2} + 2 x + 3$

문제 5

In Exercises 5–6, use the function's equation, and not its graph, to find (a) the minimum or maximum value and where it occurs. (b) the function's domain and its range. $f (x) = - x^{2} + 14 x - 106$

문제 9

Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product?

문제 10

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] $f (x) = - x^{3} + x^{2} + 2 x$

a.b. c. d.

문제 11

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).]

$f (x) = x^{6} - 6 x^{4} + 9 x^{2}$