Chapter 2

Use the given conditions to write an equation for each line in point-slope form and general form. Passing through \((-1,3)\) and parallel to the line whose equation is \(3 x-2 y-5=0\)

Find the domain of each function. $$ f(x)-\frac{1}{x+8}+\frac{3}{x-10} $$

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. \((3,-4)\) and \((3,5)\)

determine whether each relation is a function. Give the domain and range for each relation. $$ [(4,1),(5,1),(6,1)] $$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=x+3 $$

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(3.5,8.2)\( and \)(-0.5,6.2)$$

Use the given conditions to write an equation for each line in point-slope form and general form. Passing through \((4,-7)\) and perpendicular to the line whose equation is \(x-2 y-3=0\)

Find the domain of each function. $$ g(x)-\frac{1}{x^{2}+1}-\frac{1}{x^{2}-1} $$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=x+5 $$

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(2.6,1.3)\( and \)(1.6,-5.7)$$

Use the given conditions to write an equation for each line in point-slope form and general form. Passing through \((5,-9)\) and perpendicular to the line whose equation is \(x+7 y-12=0\)

Find the domain of each function. $$ g(x)-\frac{1}{x^{2}+4}-\frac{1}{x^{2}-4} $$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=2 x $$

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(0,-\sqrt{3})\( and \)(\sqrt{5}, 0)$$

Find the domain of each function. $$ h(x)-\frac{4}{\frac{3}{x}-1} $$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(-6,\) passing through \((-2,5)\)

determine whether each equation defines y as a function of \(x .\) $$ x^{2}+y-16 $$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=4 x $$

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(0,-\sqrt{2})\( and \)(\sqrt{7}, 0)$$

Find the domain of each function. $$ h(x)-\frac{5}{\frac{4}{x}-1} $$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(-8,\) passing through \((4,-1)\)

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=2 x+3 $$

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(3 \sqrt{3}, \sqrt{5})\( and \)(-\sqrt{3}, 4 \sqrt{5})$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--3,\) passing through \((-2,-3)\)

Find the domain of each function. $$ f(x)-\frac{1}{\frac{4}{x-1}-2} $$

determine whether each equation defines y as a function of \(x .\) $$ x^{2}+y^{2}-16 $$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=3 x-1 $$

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}\) \(f(x)-x^{2}-2 x\) from \(x_{1}-3\) to \(x_{2}-6\)

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(2 \sqrt{3}, \sqrt{6})\( and \)(-\sqrt{3}, 5 \sqrt{6})$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--5,\) passing through \((-4,-2)\)

Find the domain of each function. $$ f(x)-\frac{1}{\frac{4}{x-2}-3} $$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=x^{3}+2 $$

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$\left(\frac{7}{3}, \frac{1}{5}\right)\( and \)\left(\frac{1}{3}, \frac{6}{5}\right)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--4,\) passing through \((-4,0)\)

Find the domain of each function. $$ f(x)-\sqrt{x-3} $$

Determine whether each function is even, odd, or neither. $$f(x)=x^{3}+x$$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=x^{3}-1 $$

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$\left(-\frac{1}{4},-\frac{1}{7}\right)\( and \)\left(\frac{3}{4}, \frac{6}{7}\right)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--2,\) passing through \((0,-3)\)

Find the domain of each function. $$ f(x)-\sqrt{x+2} $$

Determine whether each function is even, odd, or neither. $$f(x)=x^{3}-x$$

determine whether each equation defines y as a function of \(x .\) $$ 4 x-y^{2} $$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=(x+2)^{3} $$

Write an equation in slope-intercept form of a linear function \(f\) whose graph satisfies the given conditions. The graph of \(f\) passes through \((-1,5)\) and is perpendicular to the line whose equation is \(x=6\)

Find the midpoint of each line segment with the given endpoints. $$(6,8)\( and \)(2,4)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--1,\) passing through \(\left(-\frac{1}{2},-2\right)\)

Find the domain of each function. $$ g(x)-\frac{1}{\sqrt{x-3}} $$

Determine whether each function is even, odd, or neither. $$g(x)=x^{2}+x$$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=(x-1)^{3} $$

Find the midpoint of each line segment with the given endpoints. $$(10,4)\( and \)(2,6)$$