Lesson 4

Evaluate mentally.

\(4^2\)

\(2^4\)

\(2^6\)

\(4^3\)

1. Different students are evaluating two expressions, \(3\boldcdot 6^x\) and \(5^x\). Analyze their work, describe any errors made, and then evaluate each expression correctly.

   	Noah’s work	Mai’s work	corrected work
   Evaluate \(5^x\) when \(x\) is 6.	\(5^x\) \(5^6\) 30	\(5^x\) \(5^6\) \(6 \boldcdot 6 \boldcdot 6 \boldcdot 6 \boldcdot6\) 7,776
   Evaluate \(3 \boldcdot 6^x\) when \(x\) is 2.	\(3 \boldcdot 6^x\) \(3\boldcdot 6^2\) \(3 \boldcdot 12\) 36	\(3 \boldcdot 6^x\) \(3 \boldcdot 6^2\) \(18^2\) 324

2. Here are three functions. For each function:
   1. Complete the table of values.
   2. Sketch a graph.
   3. Decide whether each function is linear, quadratic, or exponential, and be prepared to explain how you know.

   \(f(x)=3 \boldcdot 2^x\)

   \(x\)	-1	0	1	2	3	5
   \(f(x)\)

    

   

   

   \(g(x)=3 \boldcdot x^2\)

   \(x\)	-1	0	1	2	3	5
   \(g(x)\)

    

   

   

   \(h(x)=3 \boldcdot 2x\)

   \(x\)	-1	0	1	2	3	5
   \(h(x)\)

    

   

   

For each row, you and your partner will each evaluate an expression. You should each get the same answer in each row. If you disagree, work to reach agreement.

row	Partner A	PartnerB
1	\(4 \boldcdot 2^x\) when \(x\) is 3	\(2 \boldcdot 2^x\) when \(x\) is 4
2	\(19 + x^2\) when \(x\) is 9	\(4 \boldcdot x^2\) when \(x\) is 5
3	\(16 \boldcdot 2^x\) when \(x\) is 0	\(2 \boldcdot 2^x\) when \(x\) is 3
4	\(\frac12 \boldcdot 2^x\) when \(x\) is 4	\(x^2-1\) when \(x\) is 3
5	\(x^2+1\) when \(x\) is 7	\(18+2^x\) when \(x\) is 5
6	\(4+2^x\) when \(x\) is 4	\(\frac15 x^2\) when \(x\) is 10
7	\(0.1 x^2\) when \(x\) is 6	\(0.4 x^2\) when \(x\) is 3
8	\(45 \boldcdot x^2\) when \(x\) is \(\frac13\)	\(10 \boldcdot 2^x\) when \(x\) is -1
9	\(x^2\) when \(x\) is -4	\(64x^2\) when \(x\) is \(\frac12\)
10	\(\text-2 x^2\) when \(x\) is 3	\(\text-2 x^2\) when \(x\) is -3