1. Problem c) Solve the equation $|3x + 4| = |2x + 6|$. 2. Recall that for absolute values, $|A| = |B|$ implies either $A = B$ or $A = -B$. 3. Set up two equations: 1) $3x + 4 = 2x + 6$ 2) $3x + 4 = -(2x + 6)$ 4. Solve equation 1: $$3x + 4 = 2x + 6$$ Subtract $2x$ from both sides: $$x + 4 = 6$$ Subtract 4: $$x = 2$$ 5. Solve equation 2: $$3x + 4 = -2x - 6$$ Add $2x$ to both sides: $$5x + 4 = -6$$ Subtract 4: $$5x = -10$$ Divide by 5: $$x = -2$$ 6. Solutions for c) are $x = 2$ and $x = -2$. 7. Problem d) Solve the inequality $3(4 - y) \geq 9$. 8. Distribute 3: $$12 - 3y \geq 9$$ 9. Subtract 12: $$-3y \geq -3$$ 10. Divide by -3 (remember to flip inequality): $$y \leq 1$$ 11. Solution for d) is $y \leq 1$. 12. Exercise 4: Determine if graphs are functions and find domain and range. 13. Graph 1: Parabola opening upwards with vertex at $(1,-9)$. - Parabolas are functions because each $x$ has one $y$. - Domain: all real numbers, $(-\infty, \infty)$. - Range: $y \geq -9$, so $[-9, \infty)$. 14. Graph 2: Line passing through $(-1,7)$ with negative slope. - Lines are functions. - Domain: all real numbers, $(-\infty, \infty)$. - Range: all real numbers, $(-\infty, \infty)$. 15. Graph 3: V-shaped graph $y = |x| + 1$ with vertex at $(0,1)$. - Absolute value functions are functions. - Domain: all real numbers, $(-\infty, \infty)$. - Range: $y \geq 1$, so $[1, \infty)$. Final answers: - c) $x = 2$ or $x = -2$ - d) $y \leq 1$ - Graph 1: Function, Domain $(-\infty, \infty)$, Range $[-9, \infty)$ - Graph 2: Function, Domain $(-\infty, \infty)$, Range $(-\infty, \infty)$ - Graph 3: Function, Domain $(-\infty, \infty)$, Range $[1, \infty)$