Chapter 2

find the distance between each pair of points. If necessary, round answers to two decimals places. \((2,3)\) and \((14,8)\)

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=4 x \text { and } g(x)=\frac{x}{4}$$

In Exercises 1–30, find the domain of each function. $$f(x)=3(x-4)$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(4,7) \text { and }(8,10)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(1,2),(3,4),(5,5)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$(5,1) \text { and }(8,5)$$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=6 x \text { and } g(x)=\frac{x}{6}$$

Find the domain of each function. $$f(x)=2(x+5)$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(2,1) \text { and }(3,4)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(4,5),(6,7),(8,8)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (4,-1) \text { and }(-6,3) $$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=3 x+8 \text { and } g(x)=\frac{x-8}{3}$$

Find the domain of each function. $$g(x)=\frac{3}{x-4}$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(-2,1) \text { and }(2,2)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(3,4),(3,5),(4,4),(4,5)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (2,-3) \text { and }(-1,5) $$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=4 x+9 \text { and } g(x)=\frac{x-9}{4}$$

Find the domain of each function. $$g(x)=\frac{2}{x+5}$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(-1,3) \text { and }(2,4)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(5,6),(5,7),(6,6),(6,7)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (0,0) \text { and }(-3,4) $$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=5 x-9 \text { and } g(x)=\frac{x+5}{9}$$

Find the domain of each function. $$f(x)=x^{2}-2 x-15$$

In Exercises 5–8, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-8,-10)\) and parallel to the line whose equation is \(y=-4 x+3\)

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(4,-2) \text { and }(3,-2)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(3,-2),(5,-2),(7,1),(4,9)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (0,0) \text { and }(3,-4) $$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=3 x-7 \text { and } g(x)=\frac{x+3}{7}$$

Find the domain of each function. $$f(x)=x^{2}+x-12$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-7)\) and parallel to the line whose equation is \(y=-5 x+4\)

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(4,-1) \text { and }(3,-1)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(10,4),(-2,4),(-1,1),(5,6)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (-2,-6) \text { and }(3,-4) $$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=\frac{3}{x-4} \text { and } g(x)=\frac{3}{x}+4$$

Find the domain of each function. $$g(x)=\frac{3}{x^{2}-2 x-15}$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((2,-3)\) and perpendicular to the line whose equation is \(y=\frac{1}{5} x+6\)

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(-2,4) \text { and }(-1,-1)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(-3,-3),(-2,-2),(-1,-1),(0,0)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (-4,-1) \text { and }(2,-3) $$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=\frac{2}{x-5} \text { and } g(x)=\frac{2}{x}+5$$

Find the domain of each function. $$g(x)=\frac{2}{x^{2}+x-12}$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-4,2)\) and perpendicular to the line whose equation is \(y=\frac{1}{3} x+7\)

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(6,-4) \text { and }(4,-2)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(-7,-7),(-5,-5),(-3,-3),(0,0)\\} $$

find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (0,-3) \text { and }(4,1) $$

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=-x \text { and } g(x)=-x$$

Find the domain of each function. $$f(x)=\frac{1}{x+7}+\frac{3}{x-9}$$

In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general form. Passing through \((-2,2)\) and parallel to the line whose equation is \(2 x-3 y-7=0\)

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises falls, is horizontal, or is vertical. $$(5,3) \text { and }(5,-2)$$

Determine whether each relation is a function. Give the domain and range for each relation. $$ \\{(1,4),(1,5),(1,6)\\} $$