Chapter 2

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

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

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

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

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\frac{1}{x} $$

Write an equation in slope-intercept form of a linear function \(f\) whose graph satisfies the given conditions. The graph of \(f\) passes through \((-6,4)\) and is perpendicular to the line that has an \(x\) -intercept of 2 and a \(y\) -intercept of \(-4\)

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

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

Find the domain of each function. $$ g(x)-\sqrt{5 x+35} $$

Determine whether each function is even, odd, or neither. $$h(x)=x^{2}-x^{4}$$

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\frac{2}{x} $$

Write an equation in slope-intercept form of a linear function \(f\) whose graph satisfies the given conditions. The graph of \(f\) passes through \((-5,6)\) and is perpendicular to the line that has an \(x\) -intercept of \(3\) and a \(y\) -intercept of \(-9\)

Find the midpoint of each line segment with the given endpoints. $$(-4,-7)\( and \)(-1,-3)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(-\frac{1}{3},\) passing through the origin

Find the domain of each function. $$ g(x)-\sqrt{7 x-70} $$

Determine whether each function is even, odd, or neither. $$h(x)=2 x^{2}+x^{4}$$

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\sqrt{x} $$

Write an equation in slope-intercept form of a linear function \(f\) whose graph satisfies the given conditions. The graph of \(f\) is perpendicular to the line whose equation is \(3 x-2 y-4-0\) and has the same \(y\) -intercept as this line.

Find the midpoint of each line segment with the given endpoints. $$(-3,-4)\( and \)(6,-8)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--\frac{2}{3},\) passing through \((6,-2)\)

Find the domain of each function. $$ f(x)-\sqrt{24}-2 x $$

Determine whether each function is even, odd, or neither. $$f(x)=x^{2}-x^{4}+1$$

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\sqrt[3]{x} $$

Write an equation in slope-intercept form of a linear function \(f\) whose graph satisfies the given conditions. The graph of \(f\) is perpendicular to the line whose equation is \(4 x-y-6=0\) and has the same \(y\) -intercept as this line.

Find the midpoint of each line segment with the given endpoints. $$(-2,-1)\( and \)(-8,6)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope \(--\frac{3}{5},\) passing through \((10,-4)\)

Find the domain of each function. $$ f(x)-\sqrt{84-6 x} $$

Determine whether each function is even, odd, or neither. $$f(x)=2 x^{2}+x^{4}+1$$

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\frac{7}{x}-3 $$

The bar graph shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care. (Graph cant copy) Find a linear function in slope-intercept form that models the given description. Each function should model the percentage of total spending, \(p(x),\) by Americans \(x\) years after 1950. In 1950 , Americans spent \(22 \%\) of their budget on food. This has decreased at an average rate of approximately \(0.25 \%\) per year since then.

Find the midpoint of each line segment with the given endpoints. $$\left(-\frac{7}{2}, \frac{3}{2}\right)\( and \)\left(-\frac{5}{2},-\frac{11}{2}\right)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((1,2)\) and \((5,10)\)

Find the domain of each function. $$ h(x)-\sqrt{x-2}+\sqrt{x+3} $$

Determine whether each function is even, odd, or neither. $$f(x)=\frac{1}{5} x^{6}-3 x^{2}$$

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\frac{4}{x}+9 $$

The bar graph shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care. (Graph cant copy) Find a linear function in slope-intercept form that models the given description. Each function should model the percentage of total spending, \(p(x),\) by Americans \(x\) years after 1950. In 1950 , Americans spent \(3 \%\) of their budget on health care. This has increased at an average rate of approximately \(0.22 \%\) per year since then.

Find the midpoint of each line segment with the given endpoints. $$\left(-\frac{2}{5}, \frac{7}{15}\right)\( and \)\left(-\frac{2}{5},-\frac{4}{15}\right)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((3,5)\) and \((8,15)\)

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

Determine whether each function is even, odd, or neither. $$f(x)=2 x^{3}-6 x^{5}$$

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\frac{2 x+1}{x-3} $$

Find the midpoint of each line segment with the given endpoints. $$(8,3 \sqrt{5})\( and \)(-6,7 \sqrt{5})$$

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

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

Determine whether each function is even, odd, or neither. $$f(x)=x \sqrt{1-x^{2}}$$

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 $$f\left(f^{-1}(x)\right)=x \text { and } f^{-1}(f(x))=x$$ $$ f(x)=\frac{2 x-3}{x+1} $$

Find the midpoint of each line segment with the given endpoints. $$(7 \sqrt{3},-6)\( and \)(3 \sqrt{3},-2)$$

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

Find the domain of each function. $$ g(x)-\frac{\sqrt{x-3}}{x-6} $$

Determine whether each function is even, odd, or neither. $$f(x)=x^{2} \sqrt{1-x^{2}}$$