91Ó°ÊÓ

Two functions \(f\) and \(g\) can be combined by the arithmetic operations of ________, ________, ________, and _________ to create new functions.

Fill in the blanks. For an equation that represents \(y\) as a function of \(x,\) the set of all values taken on by the ___________ variable \(x\) is the domain, and the set of all values taken on by the __________ variable \(y\) is the range.

For a line, the ratio of the change in \(y\) to the change in \(x\) is called the_______ of the line

A function value \(f(a)\) is a relative _______ of \(f\) when there exists an interval \(\left(x_{1}, x_{2}\right)\) containing \(a\) such that \(x_{1}

For each function, sketch (on the same set of coordinate axes) a graph of each function for \(c=-1,1,\) and 3. (a) \(f(x)=|x|+c\) (b) \(f(x)=|x-c|\)

Find the inverse function of \(f\) informally. Verify that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=6 x$$

Determine whether the relation represents \(y\) as a function of \(x\). $$\begin{array}{|l|l|l|l|l|l|} \hline \text { Input, } x & 0 & 3 & 9 & 12 & 15 \\ \hline \text { Output, } y & 3 & 3 & 3 & 3 & 3 \\ \hline \end{array}$$

Which sets of ordered pairs represent functions from \(A\) to \(B ?\) Explain. $$A=\\{0,1,2,3\\} \text { and } B=\\{-2,-1,0,1,2\\}$$ (a) \\{(0,1),(1,-2),(2,0),(3,2)\\} (b) \\{(0,-1),(2,2),(1,-2),(3,0),(1,1)\\} (c) \\{(0,0),(1,0),(2,0),(3,0)\\} (d) \\{(0,2),(3,0),(1,1)\\}

Sketch the lines through the point with the indicated slopes on the same set of coordinate axes. Slopes (a) 0 (b) 1 (c) \(2 \quad\) (d) -3 (a) \(3 \quad\) (b) -3 (c) \(\frac{1}{2}\) (d) Undefined Point:\((2,3)\)

Determine whether each point lies on the graph of the equation. $$y=\frac{1}{3} x^{3}-2 x^{2}$$ (a) \(\left(2,-\frac{16}{3}\right)\) (b) (-3,9)