91Ó°ÊÓ

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The function \(f(x)=5\) is one-to-one.

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$h(x)=2|x+3|$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\sqrt{x-1}$$

What is the slope of a line and how is it found?

Let \(f(x)=x^{2}-x+4\) and \(g(x)=3 x-5\). Find \(g(1)\) and \(f(g(1))\).

In Exercises \(90-93,\) determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of \((x-3)^{2}+(y+5)^{2}=-36\) is a circle with radius 6 centered at \((3,-5)\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\text { If } f(x)=3 x, \text { then } f^{-1}(x)=\frac{1}{3 x}$$

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$g(x)=-2|x+4|+1$$

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$g(x)=-2|x+3|+2$$

Let \(f(x)=x^{2}-x+4\) and \(g(x)=3 x-5\). Find \(g(-1)\) and \(f(g(-1))\).