Describe how the graph of each function is related to the graph of its parent function.

5. y=-2^x+1

6. y=3^(x-4)

7. y=5^(x+1)-2

  5. reflection in y=0, translation 1 up

  6. translation 4 right

  7. translation 1 left, 2 down

Step-by-step explanation:

For parent function f(x), the transformation ...

  g(x) = a·f(x -h) +k

represents a vertical scaling by a factor of "a", a translation to the right by an amount "h", and a translation upward by an amount "k". When "a" is negative, it represents a reflection across the x-axis.

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5. a=-1, h=0, k=1. Reflection across the x-axis, then translation upward 1 unit.

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6. a=1, h=4, k=0. Translation to the right 4 units.

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7. a=1, h=-1, k=-2. Translation 1 unit left and 2 units down.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.