Name: College Algebra
Author: Lial
ISBN: 9780136881063

Ch. 3 - Polynomial and Rational Functions

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Lial 13th Edition

Ch. 3 - Polynomial and Rational Functions

Section 3.1

문제 1

Fill in the blank(s) to correctly complete each sentence. A polynomial function with leading term 3x⁵ has degree ____.

문제 3

Fill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.

문제 5

Fill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x² + 2x + 4 has x-coordinate ____ .

문제 15

Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x - 4)² - 3

문제 17

문제 19

Graph the following on the same coordinate system.

(a) y = x²

(b) y = 3x²

(d) How does the coefficient of x² affect the shape of the graph?

문제 21

Graph the following on the same coordinate system.

(a) y = (x - 2)²

(b) y = (x + 1)²

(d) How do these graphs differ from the graph of y = x²?

문제 23

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = (x - 2)²

문제 26

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = (x - 5)² - 4

문제 27

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = -(1/2)(x + 1)² - 3

문제 28

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = -3 (x - 2)² +1

문제 30

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = x² + 6x + 5

문제 34

Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. ƒ(x) = -3x² + 24x - 46

문제 37

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = (x + 3)²

문제 39

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -(x - 2)² - 5

문제 41

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = x² - 4x + 3

문제 43

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -2x² - 8x - 7

문제 44

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -3x² + 18x + 1

문제 45

Several graphs of the quadratic function ƒ(x) = ax² + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; b² - 4ac = 0

문제 47

문제 49

문제 51

Connecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.)

문제 53

Connecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.)

문제 81

Find a value of c so that y = x² - 10x + c has exactly one x-intercept.

문제 82

For what values of a does y = ax² - 8x + 4 have no x-intercepts?

문제 83

Define the quadratic function ƒ having x-intercepts (2, 0) and (5, 0) and y-intercept (0, 5).

문제 84

Define the quadratic function ƒ having x-intercepts (1, 0) and (-2, 0) and y-intercept (0, 4).

문제 85

The distance between the two points $P of open paren x sub 1 comma y sub 1 close paren$ and $R of open paren x sub 2 comma y sub 2 close paren$ is $d(P, R) = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$ . Distance formula. Find the closest point on the line $y equals 2 x$ to the point $open paren 1 comma 7 close paren$ . (Hint: Every point on $y equals 2 x$ has the form $open paren x comma 2 x close paren$ , and the closest point has the minimum distance.)

문제 86

A quadratic equation ƒ(x) = 0 has a solution x = 2. Its graph has vertex (5, 3). What is the other solution of the equation?

문제 91

Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. x² - x - 6 < 0