Just answer for free points, solved! 1. let f(x) = and g(x) = + 2which transformations are needed to transform the graph of f(x) to the graph of g(x) ? - horizontal translation 2 units left- vertical translation 1 unit down- horizontal translation 1 unit left- vertical translation 1 unit up- horizontal translation 1 unit right (correct)- vertical translation 2 units up (correct)2. let f(x) 2 + 4.the graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x) . what is the equation of g(x)? g(x) 4 + 8 3. what is the average rate of change of the function on the interval from x = 0 to x = 5? f(x) = 24.2

1. to move a function to the left by c units, add c to every x

to move a function up by c units, add c to whole function

we have from and

we added 1 to each x and added 2 to whole function

horizontal translation 1 unit left and 2 units vertical translation up

your 'correct' answers are half correct, it should be 1 unit left, not right

2.to vertically stretch a function by a fctor of c, multiply whole function by c

just multiply f(x) by 2 to get 2f(x) or

your answer is correct

3. average rate of change from (a,f(a)) to (b,f(b)) is the slope between those points

from x=0 to x=5

find f(0) and f(5)

f(0)=(1/2)(3)^0=(1/2)(1)=1/2=0.5

f(5)=(1/2)(3)^5=(1/2)(243)=121.5

slope between (0,0.5) and (5,121.5) is [tex]\frac{121.5-0.5}{5-0}=\frac{121}{5}=24.2

so you is correct