Chapter 9.4, Problem 51E

To determine

To determine which function represents the graph.

Answer to Problem 51E

The equation $m(x)=(x+2)(x+4)$ belongs to the graph given.

Explanation of Solution

Given:

Equation:

  ${}^{\begin{array}{l}h(x)={(x+2)}^2+3\\ f(x)=2(x+3)-2\\ g(x)=-\frac{1}{2}(x-8)(x-4)\\ m(x)=(x+2)(x+4)\end{array}}$

Graph:

  

Evaluation:

Graph of equation, $h(x)={(x+2)}^2+3$

  

Graph of equation, $f(x)=2(x+3)-2$

  

Graph of equation, $g(x)=-\frac{1}{2}(x-8)(x-4)$

  

Graph of equation, $m(x)=(x+2)(x+4)$

  

Conclusion:

On comparing the graphs, the equation $m(x)=(x+2)(x+4)$ belongs to the graph given.