Practice 2 Solutions

1. Write the inequality for the given graph.
   
   

$y>–\frac{4}{x}$

2. Determine if $A(2, 2), B(–2, 2), C(–2, –2), D(–5, 5)$ are solutions to the graph in problem 1.

Points A and D are solutions. B is on the dashed curve; therefore it is not a solution. Point C is not a solution because it is not in the shaded region.

3. Graph.
   $y\le –2{\left(x–3\right)}^2+4$

    

4.  

4. Graph the system of inequalities and determine the solutions.
   $$\begin{gathered} y>\sqrt{x} \\ y<–x^2 \end{gathered}$$

    

No solution

5. In which quadrant(s) would the solution be located for the quadratic inequality in problem 4 if $a=1.$

Quadrant I

6. Write the system of inequalities from the given graph.

   
   

$$\begin{gathered} y<{\left(x–2\right)}^3 \\ y>\sqrt[3]{x+3} \end{gathered}$$

7. Graph the system of inequalities.
   
8.  

8. Explain how the graph of the system would change when the absolute value inequality is $a=–\frac{2}{5}.$

The absolute value graph would open down and the shading would be below the vertex (or inside of the v-shaped graph). The shading still intersects the current shading of the parabola and is an enclosed region for the solutions.

9. Transform the system of inequalities in problem 7.

   Translate the absolute value inequality 5 spaces to the left and down 2 spaces. 
   Reflect the quadratic inequality across the x-axis and translate it up 3 spaces.
   

$$\begin{gathered} y\le \frac{2}{5}\left|x+1\right|+1 \\ y\ge –\frac{1}{3}{\left(x–2\right)}^2+3 \end{gathered}$$

10. Graph the system of inequalities from problem 9.
    
11.  

11. Graph the system of inequalities.
    $$\begin{gathered} y\le \sqrt{–x}+2 \\ y\ge 3x^2 \end{gathered}$$

     

12. Describe the solution if the parabola in problem 11 was translated 2 spaces to the right.
    

There would be no solution because the shaded regions would no longer overlap.