91Ó°ÊÓ

find the value of y if the line through the two given points is to have the indicated slope. $$(3, y) \text { and }(1,4), m=-3$$

Use a graphing utility to graph the function.Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=\operatorname{int}(x-2)$$

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

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=3 x^{2}+x+5$$

Express the given function h as a composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\) $$h(x)=|3 x-4|$$

Does \((x-3)^{2}+(y-5)^{2}=0\) represent the equation of a circle? If not, describe the graph of this equation.

find the value of y if the line through the two given points is to have the indicated slope. $$(-2, y) \text { and }(4,-4), m=\frac{1}{3}$$

Express the given function h as a composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\) $$h(x)=\frac{1}{2 x-3}$$

Use a graphing utility to graph the function.Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=|x-2|$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=-x^{2}+2 x+4$$