Chapter 2

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=x^{2}-2 $$

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)\( and \)(8,10)$$

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

If \(f(x)=2 x^{2}-5\) and \(g(x)=3 x+7,\) find: a. \((f+g)(x)\) b. \((f+g)(4)\)

In Exercises \(1-8,\) 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. $$(2,3) \text { and }(14,8)$$

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=x^{2}-1 $$

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)\( and \)(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. $$f(x)=6 x \text { and } g(x)=\frac{x}{6}$$

If \(f(x)=3 x^{2}-2 x+1\) and \(g(x)=4 x-1,\) find: a. \((f+g)(x)\) b. \((f+g)(5)\)

In Exercises \(1-8,\) 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. $$(5,1) \text { and }(8,5)$$

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=(x-2)^{2} $$

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)\( and \)(2,2)$$

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

Let \(f(x)=\sqrt{x-6}\) and \(g(x)=\sqrt{x+2},\) find: a. \((f+g)(x)\) b. the domain of \(f+g .\)

In Exercises \(1-8,\) 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. $$ (4,1) \text { and }(6,3) $$

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=(x-1)^{2} $$

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)\( and \)(2,4)$$

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

Let \(f(x)=\sqrt{x-8}\) and \(g(x)=\sqrt{x+5},\) find: a. \((f+g)(x)\) b. the domain of \(f+g .\)

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

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)=-(x-2)^{2} $$

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)\( and \)(3,-2)$$

Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=2 x+3, g(x)=x-1$$

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

In Exercises \(1-8,\) 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. $$ (0,0) \text { and }(-3,4) $$

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)=-(x-1)^{2} $$

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)\( and \)(3,-1)$$

Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=3 x-4, g(x)=x+2$$

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

In Exercises \(1-8,\) 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. $$ (0,0) \text { and }(3,-4) $$

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)=(x-2)^{2}+1 $$

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)\( and \)(-1,-1)$$

Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=x-5, g(x)=3 x^{2}$$

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

In Exercises \(1-8,\) determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,4),(1,5),(1,6)\\}$$

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

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)=(x-1)^{2}+2 $$

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)\( and \)(4,-2)$$

Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=x-6, g(x)=5 x^{2}$$

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

In Exercises \(1-8,\) determine whether each relation is a function. Give the domain and range for each relation. $$\\{(4,1),(5,1),(6,1)\\}$$

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

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=2(x-2)^{2} $$

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)\( and \)(5,-2)$$

Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=2 x^{2}-x-3, g(x)=x+1$$