Practice 1 Solutions

1. Write the inequality for the given graph.

   

$y<–\sqrt{x+2}$

2. Determine if $A(0, 0), B(2, 0), C(0, 2), D(5, –5)$ are solutions to the inequality in problem 1.

3. Graph the inequality.
   $y>\frac{1}{2}{\left(x–3\right)}^3–1$

4. Write the system of inequalities for the given graph.

   

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

5. How would the solution of the system of inequalities in problem 4 change if the absolute value graph was translated left 4 spaces?

6. Graph the system of inequalities.
   $$\begin{gathered} y>x^3 \\ y<\left|x\right| \end{gathered}$$

7. In which quadrant(s) would the solutions occur if the inequality on the absolute value in problem 6 was flipped?
   

8. Graph the inequalities and determine the solutions.
   

9. Name any asymptotes in the system. Explain why this occurs.
   

10. Reference problem 8 to write a transformed system of inequalities and graph.

    Translate the absolute value inequality right 2 spaces and down 5 spaces from its current location. Reflect the square root inequality across the y-axis.
    

11. Explain why the point $(0, 3)$ is or is not a solution to the translated graph.

12. Write the inequality for the given graph.

    

$y>\frac{6}{x}$