1. **State the problem:** Find the values for the given functions: a) Calculate $g(1) + h(-3)$ and then divide by 4. b) Calculate $\sqrt{h(-1)}$. 2. **Calculate $g(1)$:** Given $g(x) = -\frac{3}{x} + 2$, substitute $x=1$: $$g(1) = -\frac{3}{1} + 2 = -3 + 2 = -1$$ 3. **Calculate $h(-3)$:** Given $h(x) = 5x^2 - 4x$, substitute $x=-3$: $$h(-3) = 5(-3)^2 - 4(-3) = 5(9) + 12 = 45 + 12 = 57$$ 4. **Calculate $g(1) + h(-3)$:** $$-1 + 57 = 56$$ 5. **Divide by 4:** $$\frac{56}{4} = 14$$ 6. **Calculate $h(-1)$:** $$h(-1) = 5(-1)^2 - 4(-1) = 5(1) + 4 = 5 + 4 = 9$$ 7. **Calculate $\sqrt{h(-1)}$:** $$\sqrt{9} = 3$$ --- 8. **Describe the transformations for $y = f| -4(x - 6)| + 2$:** - The expression inside the absolute value is $-4(x - 6)$. - The factor $-4$ causes a vertical stretch by a factor of 4 and reflection over the y-axis inside the absolute value. - The $(x - 6)$ shifts the graph 6 units to the right. - The $+2$ outside shifts the graph 2 units upward. So, the graph is a V-shaped absolute value function shifted right 6 units, vertically stretched by 4, reflected inside the absolute value, and shifted up 2 units. --- 9. **True or False question:** "A function can have more than 1 y-intercept." This is false because a function must pass the vertical line test, which means it can only cross the y-axis once. Multiple y-intercepts would violate this rule. **Final answers:** a) $\frac{g(1) + h(-3)}{4} = 14$ b) $\sqrt{h(-1)} = 3$ c) Transformations: shift right 6, vertical stretch by 4, reflection inside absolute value, shift up 2. d) False, a function cannot have more than one y-intercept.