Lesson 20

1. Find the slope of each line.
   1. The line that passes through $(2,2)$ and $(3,6)$.
   2. The graph of $f(x)=\text-2+\frac13x$.
2. Show on the graph where each slope can be seen.

 

1. For the function $f(x)=3x+4$, evaluate:
   1. $f(0)$ and $f(1)$
   2. $f(100)$ and $f(101)$
   3. $f(\text-10)$ and $f(\text-9)$
   4. $f(0.5)$ and $f(1.5)$
2. What do all those pairs of numbers you found have in common?
3. Write an expression for $f(w)$ and $f(w+1)$.
4. What would you expect to be the result of subtracting $f(w)$ from $f(w+1)$?
5. Subtract $f(w)$ from $f(w+1)$. If you don’t get the answer you predicted, work with a partner to check your algebra.
6. For the function $g(x)=2^x$, evaluate:
   1. $g(3)$ and $g(4)$
   2. $g(0)$ and $g(1)$
   3. $g(\text-1)$ and $g(\text-2)$
   4. $g(10)$ and $g(11)$
7. What do all those pairs of numbers you found have in common?
8. Write an expression for $g(u)$ and $g(u+1)$.
9. What would you expect to be the result of dividing $g(u+1)$ by $g(u)$?
10. Divide $g(u+1)$ by $g(u)$. If you don’t get the answer you predicted, work with a partner to check your algebra.

1. Evaluate:
   1. $\dfrac{3^5}{3^4}$
   2. $\dfrac{3^1}{3^0}$
   3. $\dfrac{3^{\text-1}}{3^{\text-2}}$
   4. $\dfrac{3^{100}}{3^{99}}$
   5. $\dfrac{3^{x+1}}{3^x}$
2. Solve for $m$:
   1. $\dfrac{2^m}{2^7}=2$
   2. $\dfrac{2^{100}}{2^m}=2$
   3. $\dfrac{2^m}{2^x}=2$
3. Write an equivalent expression using as few terms as possible:
   1. $3(x+1) + 4 - (3x + 4)$
   2. $2(x+1) + 5 - (2x + 5)$
   3. $2(x+2) + 5 - (2(x+1) + 5)$
   4. $\text-5(x+1) + 3 - (\text-5x + 3)$
   5. $\dfrac{5^{x+1}}{5^x}$
   6. $\dfrac{7^{x+4}}{7^x}$