Question 108601: How would I answer these problems I am really stuck. Any help would be greatly appreciated. Thank you.
Suppose the graph of y = x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
a)  (Cannot copy and paste this graph)for this parablola
Answer: g(x) = (x + 1)^2 – 3 (vertical shift down 3 units) Y = X^2 - 3
Is this right???
b)  x , y, axis U shape goes right over 4 on the x axis
Answer: g(x) = (x – 4)^2 (horizontal shift right 4 units) Is this right???
3) Consider the following graph of y = f(x).
a) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form.
Answer:
b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form.
Answer:
4) Consider the function: f(x)= x^2+ 4x + 1
a) Find h, the x-coordinate of the vertex of this parabola.
Answer:
Show your work here:
b) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.
Answer:
x y
h =__
c) Use MS Excel to graph the function by plotting the points found in the table in part b.
Answer:
5) Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.
a)f(x)= 2x+3/x+2
Answer:
Horizontal:
Vertical:
b)g(x)= 5x/x^2+1
Answer:
Horizontal:
Vertical:
c)
Answer:
Horizontal:
Vertical:
d)
Answer:
Horizontal:
Vertical:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How would I answer these problems I am really stuck. Any help would be greatly appreciated. Thank you.
Suppose the graph of y = x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
a)g(x) = (x + 1)^2 – 3
The (x+1) moves each point of y=x^2 one to the left
The -3 moves the result of the 1st move down three.
 graph(400,300,-10,10,-10,10,(x+1)^2-3
------------------------------
Answer: b) x , y, axis U shape goes right over 4 on the x axis
Answer: g(x) = (x – 4)^2 (horizontal shift right 4 units) Is this right???
Yes, that is correct.
-----------------------------------
3) Consider the following graph of y = f(x).
a) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form.
Answer: (x, f(x)+2)
------------------------
b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form.
Answer: That depends on what line you reflect in:
If you reflect in the y-axis the answer is (-x,h(x))
If you reflect in the x-axis the anser is (x,-h(x))
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4) Consider the function: f(x)= x^2+ 4x + 1
a) Find h, the x-coordinate of the vertex of this parabola.
Answer: (-2,-3)
Show your work here:
Complete the square on the x-terms:
x^2+4x +? = f(x)-1+?
x^2+4x+4 = f(x)+3
(x+2)^2 = f(x)+3
-----------------------------
b) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.
Answer:
f(x)= x^2+ 4x + 1
x y
If x = -4, y = 16-16+1 = 1
If x = -3, y = 9-12+1 = -2
If x = -1, y = 1-4+1 = -2
If x = 0, y = 0+0+1 = 1
h =__
=====================
c) Use MS Excel to graph the function by plotting the points found in the table in part b.
Answer:
I'll leave that to you.
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5) Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.
a)f(x)= 2x+3/x+2
Answer:
Horizontal:y = 2x/x = 2
Vertical: x = -2
------------------
b)g(x)= 5x/x^2+1
Answer:
Horizontal: y = 0x^2/x^2 = 0
Vertical: none since x^2+1 cannot be zero
---------------------
c)
Answer:
Horizontal:
Vertical:
d)
Answer:
Horizontal:
Vertical:
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Cheers,
Stan H.
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