What is the horizontal shift for the absolute value function below? Explain how you know using complete sentences. Include the direction and number of units of the shift. ( 3 points) \( f(x)=3|x+6|+9 \) \[ \begin{array}{l}|x+6| x+6=x-(-6) H=-6-6 \text { is shifted to the left by } 6 \text { units. } \\ \text { Standard form of an absolute value function is } f(x)=a|x-h|+k \\ \text { H indicates horizontal shift. }\end{array} \]

Level 5-6 Questions (Revised with Negative Powers of 10): 1. Find the sum \( \left(5 \times 10^{7}\right)+\left(3.2 \times 10^{6}\right) \) in standard form. 2. Subtract \( \left(1.2 \times 10^{4}\right)-\left(5 \times 10^{3}\right) \) and express in scientific notation 3. Add \( \left(8.1 \times 10^{-2}\right)+\left(4.9 \times 10^{-3}\right) \) and express in scientific notatio 4. Find the difference \( \left(3.6 \times 10^{-4}\right)-\left(2.1 \times 10^{-5}\right) \) in standard form. 5. Multiply \( \left(2 \times 10^{8}\right) \cdot\left(5.5 \times 10^{-3}\right) \) and express in scientific notation. 6. Divide \( \left(6.4 \times 10^{9}\right) \div\left(8 \times 10^{-4}\right) \) in scientific notation. 7. Add \( \left(7.2 \times 10^{8}\right)+\left(3 \times 10^{-2}\right) \) in scientific notation. 8. Subtract \( \left(9.8 \times 10^{7}\right)-\left(2.3 \times 10^{-3}\right) \) and write in standard form. 9. Multiply \( \left(3.5 \times 10^{-5}\right) \cdot\left(2 \times 10^{3}\right) \) in scientific notation. 10. Divide \( \left(5.6 \times 10^{9}\right) \div\left(4 \times 10^{-3}\right) \) in scientific notation.

Suppose we have two functions: \( f(x)=x^{2}+1 \) and \( g(x)=3 x+5 \) Find the value of \( f(-1) g(-1) \). 11 16

If \( x \) is multiplied by 5 and then 3 is subtracted, then the function is \( f(x)=5 x-3 \). What are the steps to find the inverse to this function? a.) Multiply by 3 , then subtract 5 b.) Subtract by 5 , then multiply by 3 c.) Add 3 , then divide by 5 d.) Divide by 5 , then add 3

8. \( \int \frac{x+\pi}{x^{2}-3 \pi x+2 \pi^{2}} d x \)

2 Represent the function \( V(x) \) using technology. Determine the domain and range of the function. Determine the domain and range of the function as they relate to this problem situation. Explain your reasoning.