www.AlgebraNation.com Section 3 Topic 5  

Name _______________________________________________ Date ______________ Introduction to Functions Dividing Functions Independent Practice For exercises 1-3, rewrite the equations as systems (equations and constraints). Do not solve.

1.   Let 𝑓 𝑥 = 4𝑥−4. Find values for 𝑥 for which 𝑓 𝑥 = 2.

2.   Let 𝑔 𝑥 = 27𝑥2= 3. Find values for 𝑥 for which 𝑔 𝑥 = 3.

3.   Let 𝑚 𝑥 = 5𝑥 and ℎ(𝑥) = 25

𝑥+8. Find values for 𝑥 for which 𝑚 𝑥 = ℎ(𝑥).

www.AlgebraNation.com Section 3 Topic 5  

For exercises 4-7, rewrite each equation as a system of equations and then solve.

4.   𝑓 𝑥 = 𝑥 − 3 and 𝑔 𝑥 = 𝑥 + 9. Find values of 𝑥 for which 2(3)4(3)

= 0.

5.   𝑓 𝑥 = 2𝑥 and 𝑔 𝑥 = 3

𝑥−3. Find values of 𝑥 for which 𝑓(𝑥) = 𝑔(𝑥).

6.   𝑓 𝑥 = 𝑥 + 8 and 𝑔 𝑥 = 𝑥 + 8. Find values of 𝑥 for which 2(3)4(3)

= 32.

7.   𝑓 𝑥 = 𝑥𝑥−1. Find values of 𝑥 for which 𝑓(𝑥) = 2

3.

www.AlgebraNation.com Section 3 Topic 5  

8.   Shaquille goes on a four mile run each Sunday. His run typically takes 38 minutes. He wants to increase this distance to 7 miles. Part A: Write and solve an algebraic equation to find the time it would take

him to run 7 miles. Part B: How long would it take him to run a marathon (26.2 miles)?

9.  Consider the following equation 9:3= ;

3<;. Select all that apply.

¨   𝑥 ≠ −3 ¨   𝑥 ≠ 0 ¨   𝑥 ≠ −2 ¨   𝑥 ≠ 2 ¨   𝑥 = 10 ¨   𝑥 = 2

10.  Consider the following equation 3<>>3<>>

= 1. Select all that apply.

¨   No solutions ¨   All real numbers and 𝑥 ≠ −11 ¨   All real numbers and 𝑥 ≠ 11 ¨   𝑥 = 1 ¨   𝑥 = −11

www.AlgebraNation.com Section 3 Topic 5  

11.  The Moss Family are horse racing fans, breeders and owners. They own the champion mare and horse of the year, Zenyatta. They commissioned an artist to create a model of the champion horse to be displayed at their farm. The model was made to scale and is shown below.

What is the value, in inches, of 𝑧? If necessary, round to the nearest tenth of an inch.

9