91Ó°ÊÓ

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ h(x)=-|x+3| $$

In Exercises \(21-32,\) evaluate each function at the given values of the independent variable and simplify. $$f(x)=\frac{4 x^{3}+1}{x^{3}}$$ a. \(f(2)\) b. \(f(-2) \quad\) c. \(f(-x)\)

Find the midpoint of each line segment with the given endpoints. $$ (\sqrt{50},-6) \text { and }(\sqrt{2}, 6) $$

Find: a. \((f \circ g)(x)\) b. the domain of \(f \circ g\) $$f(x)=\frac{5}{x+4}, g(x)=\frac{1}{x}$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-4)\) and \((1,-1)\)

In Exercises \(21-32,\) evaluate each function at the given values of the independent variable and simplify. $$f(x)=\frac{x}{|x|}$$ a. \(f(6)\) b. \(f(-6)\) c. \(f\left(r^{2}\right)\)

Write the standard form of the equation of the circle with the given center and radius. $$ \text { Center }(0,0), r=7 $$

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ g(x)=-|x+4|+1 $$

Find: a. \((f \circ g)(x)\) b. the domain of \(f \circ g\) $$f(x)=\frac{x}{x+1}, g(x)=\frac{4}{x}$$

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