Question: Suppose $f(x)=20x+14$. 1. Suppose $F(x)$ is the graph of $f(x)$ shifted right by 9 units. Write the formula for $F(x)$. $F(x)=$ 2. Suppose $F(x)$ is the graph of $f(x)$ shifted left by 6 units. Write the formula for $F(x)$. $F(x)=$ 3. Suppose $F(x)$ is the graph of $f(x)$ shifted up by 7 units. Write the formula for $F(x)$. $F(x)=$ 4. Suppose $F(x)$ is the graph of $f(x)$ shifted down by 4 units. Write the formula for $F(x)$. $F(x)=$ Suppose $g(x)=x^2+11x-19$. 5. Suppose $G(x)$ is the graph of $g(x)$ shifted right by 5 units. Write the formula for $G(x)$. $G(x)=$ 6. Suppose $G(x)$ is the graph of $g(x)$ shifted left by 2 units. Write the formula for $G(x)$. $G(x)=$ 7. Suppose $G(x)$ is the graph of $g(x)$ shifted up by 9 units. Write the formula for $G(x)$. $G(x)=$ 8. Suppose $G(x)$ is the graph of $g(x)$ shifted down by 2 units. Write the formula for $G(x)$.

1. **Problem:** Find the formula for $F(x)$ when $f(x)=20x+14$ is shifted right by 9 units. **Rule:** Shifting right by $h$ units means replacing $x$ by $x - h$. $$F(x) = f(x-9) = 20(x-9) + 14$$ Simplify: $$F(x) = 20x - 180 + 14 = 20x - 166$$ 2. **Problem:** Find the formula for $F(x)$ when $f(x)=20x+14$ is shifted left by 6 units. **Rule:** Shifting left by $h$ units means replacing $x$ by $x + h$. $$F(x) = f(x+6) = 20(x+6) + 14$$ Simplify: $$F(x) = 20x + 120 + 14 = 20x + 134$$ 3. **Problem:** Find the formula for $F(x)$ when $f(x)=20x+14$ is shifted up by 7 units. **Rule:** Shifting up by $k$ units means adding $k$ to the function. $$F(x) = f(x) + 7 = 20x + 14 + 7 = 20x + 21$$ 4. **Problem:** Find the formula for $F(x)$ when $f(x)=20x+14$ is shifted down by 4 units. **Rule:** Shifting down by $k$ units means subtracting $k$ from the function. $$F(x) = f(x) - 4 = 20x + 14 - 4 = 20x + 10$$ 5. **Problem:** Find the formula for $G(x)$ when $g(x)=x^2 + 11x - 19$ is shifted right by 5 units. **Rule:** Shift right by $h$ units means replace $x$ by $x - h$. $$G(x) = g(x-5) = (x-5)^2 + 11(x-5) - 19$$ Expand: $$(x-5)^2 = x^2 - 2\cdot5x + 25 = x^2 - 10x + 25$$ $$11(x-5) = 11x - 55$$ So, $$G(x) = x^2 - 10x + 25 + 11x - 55 - 19 = x^2 + ( -10x + 11x ) + (25 - 55 - 19)$$ Simplify: $$G(x) = x^2 + x - 49$$ 6. **Problem:** Find the formula for $G(x)$ when $g(x)=x^2 + 11x - 19$ is shifted left by 2 units. **Rule:** Shift left by $h$ units means replace $x$ by $x + h$. $$G(x) = g(x+2) = (x+2)^2 + 11(x+2) - 19$$ Expand: $$(x+2)^2 = x^2 + 2\cdot2x + 4 = x^2 + 4x + 4$$ $$11(x+2) = 11x + 22$$ So, $$G(x) = x^2 + 4x + 4 + 11x + 22 - 19 = x^2 + (4x + 11x) + (4 + 22 - 19)$$ Simplify: $$G(x) = x^2 + 15x + 7$$ 7. **Problem:** Find the formula for $G(x)$ when $g(x)=x^2 + 11x - 19$ is shifted up by 9 units. **Rule:** Shift up by $k$ units means add $k$ to the function. $$G(x) = g(x) + 9 = x^2 + 11x - 19 + 9 = x^2 + 11x - 10$$ 8. **Problem:** Find the formula for $G(x)$ when $g(x)=x^2 + 11x - 19$ is shifted down by 2 units. **Rule:** Shift down by $k$ units means subtract $k$ from the function. $$G(x) = g(x) - 2 = x^2 + 11x - 19 - 2 = x^2 + 11x - 21$$