SOLUTION: i need help understanding step by step with these problems they are all odd in my book answers are in the back of book i would like to know how to solve them not just the answer. t

Question 149294This question is from textbook college algebra
: i need help understanding step by step with these problems they are all odd in my book answers are in the back of book i would like to know how to solve them not just the answer. thanks a bunch.
(#33-47) Sketch the graph of the function, not by plotting points,but by starting with teh graph of a standard function and applying transofrmation.
#33....f(x)= (x-2)^2 (the answer is a parabola going upward)
#35....f(x)= - (x+1)^2 (the answer is a parabola going downward)
#37....f(x)= x^3 +2 (the answer is a wiggly line from neg side to positive side like a snake)
#39....y = 1 + sqrt of (x)(the answer is half of a line on the positive side)
#41...y = (1)/(2) squaroot (x+4) then minus 3 (the answer is a closed circle going from negative side to negative side on the positive side)
#43....y = 5 + (x +3)^2 (the answer is a parabola on the negative positive side)
#45...y = /x/ - 1 (the answer is shape like a "v")
$47...y = /x + 2 / +2 (the answer is shape like a "v" just not touching the (0,0)) This question is from textbook college algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i need help understanding step by step with these problems they are all odd in my book answers are in the back of book i would like to know how to solve them not just the answer. thanks a bunch.
(#33-47) Sketch the graph of the function, not by plotting points,but by starting with the graph of a standard function and applying transformation.
The standard form you want is y = x^2 which is a parabola opening upward
with its vertex at (0,0)
-----------------------------------------------

#33....f(x)= (x-2)^2 (the answer is a parabola going upward)
The graph of this function is the same as y = x^2 but each point
is moved 2 to the right; for example the vertex is now at (2,0)
-----------------------------------------------
#35....f(x)= - (x+1)^2 (the answer is a parabola going downward)
This sketch is y = x^2 flipped over on the x-axis so it opens
downward, with each point moved 1 to the left so the vertex is
now at (-1,0)
-----------------------------------------------
#37....f(x)= x^3 +2 (the answer is a wiggly line from neg side to positive side like a snake)
The standard graph is that of y = x^3.
Your graph looks like the standard graph but each point is 2 higher.
-----------------------------------------------
#39....y = 1 + sqrt of (x)(the answer is half of a line on the positive side)
The standard is y = sqrt(x)
Yours has all points moved 1 higher
----------------------------------------
#41...y = (1/2)sqrt(x+4) then minus 3 (the answer is a closed circle going from negative side to negative side on the positive side)
The standard graph is y = sqrt(x)
Yours has all points moved 4 to the left, the standard's y-values are multiplied
by (1/2).
-----------------------
#43....y = 5 + (x +3)^2 (the answer is a parabola on the negative positive side)
The standard is y = x^2.
Yours has all points moved 3 to the left then 5 added to their y value.
---------------------------
#45...y = /x/ - 1 (the answer is shape like a "v")
The standard is y = |x|
Yours lowers each point by 1.
---------------------------
$47...y = /x + 2 / +2 (the answer is shape like a "v" just not touching the (0,0))
Standard is y = |x|
Yours has all point moved 2 to the left then raised by 2.
---------------------------
Cheers,
Stan H.

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