# 1.8: Functions and Mathematical Models

Difficulty Level:

**At Grade**Created by: CK-12Turn In

## Review Answers

- (1/2)
*x*^{2}+5*x*+5 - (1/2)
*x*^{2}-3*x*+5 - 2
*x*^{3}+ (3/2)*x*^{2}-5*x* -
\begin{align*}h(x)=\frac {4x-5}{\frac {1}{2}x^2+x} = \frac {8x-10}{x^2+2x}\end{align*}
h(x)=4x−512x2+x=8x−10x2+2x . The domain is the set of all real numbers, except x ≠ 0,x ≠ -2. -
*f*(*g*(*x*))=*f*(*x*+8)=(*x*+8)^{3}*g*(*f*(*x*))=*g*(*x*^{3})=*x*^{3}+8 They are never equal. - The graph of
*f*(*g*(*x*)) is the graph of*f*(*x*), shifted 8 units to the left. - 20
*x*-59 -
*g*(*x*)=3*x*+1,*h*(*x*)=*x*^{4},*t*(*x*)=*f*(*g*(*x*)) -
The domain of
*f+g*is \begin{align*}\mathbb R\end{align*}. The range is*y*≤ 3.25. (g/f) has the domain of all real numbers except*x*=0. The range is all real numbers. -
*f*(*g*(*x*))= (*dx*+*a*)/(*bdx+c*). The domain of the function is all real numbers except*x*= (-*c*)/*bd*.

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Date Created:

Feb 23, 2012
Last Modified:

Apr 19, 2016
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