Question

This is one question. Algebra 2 transformations

Answer 1

Explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x - n) - shift the graph n units to the right

f(x + n) - shift the graph n units to the left

f(-x) - reflection over the y-axis

-f(x) - Reflection over the x-axis

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f(x) = ln(x)

1. 2 units up → f(x) + 2 = ln(x) + 2

2. 2 units right → f(x - 2) = ln(x - 2)

3. 2 units left → f(x + 2) = ln(x + 2)

4. Reflect y-axis → f(-x) = ln(-x)

If these are further transformations of the graph, then:

1. f(x) + 2 = ln(x) + 2

2. f(x - 2) + 2 = ln(x - 2) + 2

3. f(x - 2 + 2) + 2 = f(x) + 2 = ln(x) + 2

4. f(x) + 2 - 2 = f(x) = ln(x)

5. f(-x) = ln(-x)

Answer 2

End result is ln(-x) + 1

Explanation:

1, ln x + 2

2. ln(x + 2) + 2

3. ln(x + 2 - 2) + 2 = ln x + 2

4. ln x + 1

5. ln(-x) + 1