Lial - College Algebra 13th Edition

Ch. 2 - Graphs and Functions

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Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 23

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. vertical, through (-6, 4)

Problem 23

Determine whether the three points are the vertices of a right triangle. (-6,-4),(0,-2),(-10,8)

Problem 23

Determine whether each relation defines a function, and give the domain and range.

Problem 23

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} 4 - x & if x < 2 \\ 1 + 2 x & if x \geq 2 \end{matrix}$

Problem 23a

For the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2.

ƒ(x)=√(4x-1), g(x)=1/x

Problem 23b

For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.

ƒ(x)=√(4x-1), g(x)=1/x

Problem 23c

For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.

ƒ(x)=√(4x-1), g(x)=1/x

Problem 23d

For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2.

ƒ(x)=√(4x-1), g(x)=1/x

Problem 24

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

Problem 24

Determine whether the three points are the vertices of a right triangle. See Example 3.

$(- 2, - 8), (0, - 4), (- 4, - 7)$

Problem 24

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} 2 x + 1 & if x \geq 0 \\ x & if x < 0 \end{matrix}$

Problem 24

For the pair of functions defined, find (ƒ+g)(x), (ƒ-g)(x), (ƒg)(x), and (f/g)(x).Give the domain of each. ƒ(x)=√(5x-4), g(x)=-(1/x)

Problem 24

Determine whether each relation defines a function, and give the domain and range.

Problem 25

Determine whether the three points are the vertices of a right triangle. (-4,1),(1,4),(-6,-1)

Problem 25

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. horizontal, through (-7,4)

Problem 25

Graph each piecewise-defined function.

$f (x) = {\begin{matrix} - 3 & if x \leq 1 \\ - 1 & if x > 1 \end{matrix}$

Problem 25

Graph each function. See Examples 1 and 2. ƒ(x)=-(1/2)x²

Problem 25

Determine whether each equation defines y as a function of x. y = 6 -x²

Problem 25

Use each graph to determine an equation of the circle in (a) center-radius form and (b) general form.

Problem 26

Graph each line. Give the domain and range. x = -4

Problem 26

Determine whether each equation defines y as a function of x. x = (1/3)(y²)

Problem 26

Determine whether the three points are the vertices of a right triangle. See Example 3.

$(- 2, - 5), (1, 7), (3, 15)$

Problem 27

Give the center and radius of the circle represented by each equation. x²+y²+6x+8y+9=0

Problem 27

Determine whether each equation defines y as a function of x. y = ±√(x-2)

Problem 27

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. m=5, b=15

Problem 27

Graph each function. See Examples 1 and 2. ƒ(x)=-3|x|

Problem 27

Determine whether the three points are the vertices of a right triangle. (-4,3),(2,5),(-1,-6)

Problem 27

Determine whether each relation defines a function, and give the domain and range.

Problem 28

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

Problem 28

Graph each line. Give the domain and range. -3x + 6 = 0