Lesson 4 Pulling a Rabbit Out of the Hat Solidify Understanding

Ready

Use the product rule or the quotient rule to rewrite the expression. Leave all answers in exponential form with only positive exponents.

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Set

13.

Given the functions and :

a.

Calculate and .

b.

What do your ordered pairs for and imply?

c.

Find .

d.

Based on your answer for , predict .

e.

Find . Did your answer match your prediction?

f.

Are and inverse functions? Justify your answer.

14.

  1. ___

  2. ___

  3. ___

  4. ___

  5. ___

  6. ___

  7. ___

Go

Calculate and for each pair of functions.

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19.

Match each graph with the correct pair of functions from problems 15–18. Label and .

Then, graph the line on each of the graphs.

a.

The graph matches functions from #:

Graph the line on the graph.

Two transformed functions of 1/xx–5–5–5555y–5–5–5555000

b.

The graph matches functions from #:

Graph the line on the graph.

Two linear functions that are not intersecting.x–10–10–10–5–5–5555101010y–10–10–10–5–5–5555101010000

c.

The graph matches functions from #:

Graph the line on the graph.

Two cubic functions intersecting at about (-3.5,-3.5)x–5–5–5555y–5–5–5555000

d.

The graph matches functions from #:

Graph the line on the graph.

two linear functions intersecting at (-5,-5)x–5–5–5555y–5–5–5555000

e.

Look back at the lines on each of the graphs. What do you notice?

20.

Do you think your observations about the graphs in #19 has anything to do with the answers you got when you found and ? Explain.

21.

Look again at the graph from #19b.

a.

Shade the 2 triangles made by the -axis, -axis, and each line.

Two linear functions that are not intersecting.x–10–10–10–5–5–5555101010y–10–10–10–5–5–5555101010000

b.

What is interesting about these two triangles?

22.

Look again at the graph from #19d.

a.

Shade the 2 triangles in the graph.

two linear functions intersecting at (-5,-5)x–5–5–5555y–5–5–5555000

b.

Are they interesting in the same way? Explain.