91Ó°ÊÓ

If \(f(x)=x^{3}-5\) and \(g(x)=\sqrt[3]{x+5},\) find a. \(\quad f(g(x))\) b. \(g(f(x))\) c. What does this tell us about the relationship between \(f(x)\) and \(g(x) ?\)

Given each function, evaluate: \(f(-1), f(0), f(2), f(4)\). $$ f(x)=\left\\{\begin{array}{ccc} x^{3}+1 & \text { if } & x<0 \\ 4 & \text { if } & 0 \leq x \leq 3 \\ 3 x+1 & \text { if } & x>3 \end{array}\right. $$

Sketch a graph of each function as a transformation of a toolkit function. $$ m(t)=3+\sqrt{t+2} $$

If \(f(x)=\frac{x}{2+x}\) and \(g(x)=\frac{2 x}{1-x},\) find a. \(\quad f(g(x))\) b. \(g(f(x))\) c. What does this tell us about the relationship between \(f(x)\) and \(g(x)\) ?

Sketch a graph of each piecewise function. $$ f(x)=\left\\{\begin{array}{ccc} |x| & \text { if } & x<2 \\ 5 & \text { if } & x \geq 2 \end{array}\right. $$

Sketch a graph of each piecewise function. $$ f(x)=\left\\{\begin{array}{lll} 4 & \text { if } & x<0 \\ \sqrt{x} & \text { if } & x \geq 0 \end{array}\right. $$

Sketch a graph of each piecewise function. $$ f(x)=\left\\{\begin{array}{cll} x^{2} & \text { if } & x<0 \\ x+2 & \text { if } & x \geq 0 \end{array}\right. $$

Starting with the graph of \(f(x)=6^{x}\) write the equation of the graph that results from a. reflecting \(f(x)\) about the \(x\) -axis and the \(y\) -axis b. reflecting \(f(x)\) about the \(x\) -axis, shifting left 2 units, and down 3 units

Starting with the graph of \(f(x)=4^{x}\) write the equation of the graph that results from a. reflecting \(f(x)\) about the \(x\) -axis b. reflecting \(f(x)\) about the \(y\) -axis, shifting right 4 units, and up 2 units

Sketch a graph of each piecewise function. $$ f(x)=\left\\{\begin{array}{ccc} x+1 & \text { if } & x<1 \\ x^{3} & \text { if } & x \geq 1 \end{array}\right. $$