Chapter 2.2, Problem 105E

To determine

(a)

To sketch:

The graph of function $f\left(x\right)=x^4$, explain how the graph of function $g\left(x\right)=f\left(x\right)+2$ differs from the graph f and determine whether g is even, odd or neither.

To determine

(b)

To explain:

The translations of graph of function $g\left(x\right)=f\left(x\right)+2$ from the graph f and determine whether g is even, odd or neither.

To determine

(c)

To explain:

The translations of graph of function $g\left(x\right)=f\left(-x\right)$ from the graph f and determine whether g is even, odd or neither.

To determine

(d)

To explain:

The translations of graph of function $g\left(x\right)=-f\left(x\right)$ from the graph f and determine whether g is even, odd or neither.

To determine

(e)

To explain:

The translations of graph of function $g\left(x\right)=f\left(\frac{1}{2}x\right)$ from the graph f and determine whether g is even, odd or neither.

To determine

(f)

To explain:

The translations of graph of function $g\left(x\right)=\frac{1}{2}f\left(x\right)$ from the graph f and determine whether g is even, odd or neither.

To determine

(g)

To explain:

The translations of graph of function $g\left(x\right)=f\left(x^{\frac{3}{4}}\right)$ from the graph f and determine whether g is even, odd or neither.

To determine

(h)

To explain:

The translations of graph of function $g\left(x\right)=\left(f\circ f\right)\left(x\right)$ from the graph f and determine whether g is even, odd or neither.