Multiple part question!

Question

(a) Explain how the graph of the function y=3log₂x+2 can be obtained from the graph of y=log₂x.

(b) Graph the function y=3log₂x+2.

(c) Choose the correct answer below.

The graph is stretched vertically by a factor of 3 and shifted 2 units downward.

The graph is stretched vertically by a factor of 3 and shifted 2 units upward.

The graph is shrinking vertically by a factor of 3 and shifted 2 units downward.

The graph is shrinking vertically by a factor of 3 and shifted 2 units upward.

Answer 1

First graph y=log2(x)

For 3log2(x) +2. You are stretching by a factor of 3 and vertically shifting 3 up so every y value if first multiplied by 3 and the you add 2

lets look at some key points on the graph of the parent function (1,0)(2,1)(4,2)(8,3) now keeping the x value the same multiply y by 3 and add 2 this gives you

(1,2)(2,5)(4,8)(8,11). Plot these points and you have your graph