91Ó°ÊÓ

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=|x|,\) but stretched horizontally by a factor of 2 and shifted down 5 units

Graph each of the following functions. Check your results using a graphing calculator. $$f(x)=\left\\{\begin{array}{ll} 4, & \text { for } x \leq-2 \\ x+1, & \text { for }-2

For each function \(f,\) construct and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ $$f(x)=\frac{1}{2 x}$$

Consider the following linear equations. Without graphing them, answer the questions below. a) \(y=x\) \(\quad\) b) \(y=-5 x+4\) \(\quad\) c) \(y=\frac{2}{3} x+1\) \(\quad\) d) \(y=-0.1 x+6\) \(\quad\) e) \(y=3 x-5\) \(\quad\) f) \(y=-x-1\) \(\quad\) g) \(2 x-3 y=6\) \(\quad\) h) \(6 x+3 y=9\) Which slope down from left to right?

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=\sqrt{x},\) but reflected across the \(y\) -axis and shifted left 2 units and down 1 unit

Graph each of the following functions. Check your results using a graphing calculator. $$g(x)=\left\\{\begin{array}{ll} \frac{1}{2} x-1, & \text { for } x<0 \\ 3, & \text { for } 0 \leq x \leq 1 \\ -2 x, & \text { for } x>1 \end{array}\right.$$

For each function \(f,\) construct and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ $$f(x)=-\frac{1}{4 x}$$

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=1 / x,\) but reflected across the \(x\) -axis and shifted up 1 unit

Graph each of the following functions. Check your results using a graphing calculator. $$f(x)=\left\\{\begin{array}{ll} \frac{x^{2}-9}{x+3}, & \text { for } x \neq-3 \\ 5, & \text { for } x=-3 \end{array}\right.$$

For each function \(f,\) construct and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ $$f(x)=-\frac{1}{x}$$