please help me as soon as possible. please

Question

Question 1.) Identify the scatter plot of the data. Treat the number of girls in the class as the independent variable.

Data Table:

Class: I II III IV V VI VII VIII IX

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Girls: 5 14 16 8 20 21 25 30 29

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Boys: 15 10 10 19 20 23 25 12 6

A.)

B.)

C.)

D.)

Question 2.) Let g(x) be the indicated transformation of f(x) = |4x| − 5. Compress the graph of f(x) = |4x| − 5 horizontally by a factor of 1/2 and reflect it across the x-axis. Identify the rule and graph of g(x).

A.)

g(x) = −|8x| + 5

B.)

g(x) = |8x| − 5

C.)

g(x) = −|8x| + 5

D.)

g(x) = |8x| − 5

Please give solution and explanation please.

Answer 1

1.) By looking at the table, Choice C is best represented as a scatter data with number of girls as an independent (explanatory) variable.

2.) f(x) = |4x| - 5

Compressed horizontally by a factor of 1/2 → |4/(1/2)x| - 5 = |(4*2)x| - 5 = |8x| - 5

Reflect across the x-axis → - (|8x| - 5) = - |8x| + 5 (negative sign in front of the absolute value function and distribute the negative sign to each term)

In this case, Choice C is the correct answer.

Answer 2

question #1 looks like option A

question #2

(-2)|4x| - 5

(-2) |4||x|- 5 =

(-2)(4) |x| -5 =

-8|x|-5 =

- |8||x|-5 =

- |8x|-5

so option C