# If The Function Y=3 - 2x Is Shifted Right 1 And Down3 What Is The Resulting Function Show Work .

Given the function f(x) = x^3 + x^2 − 2x + 1, what is the resulting function when f(x) is shifted to the left 1 unit?

f(x) = x³ + x² − 2x + 1

// To shift this function 1 unit to the LEFT,
// you need to replace x by (x+1)
// (Look at the 3 sample graphs of y=x² below)

f(x+1) = (x+1)³ + (x+1)² − 2(x+1) + 1

f(x+1) = (x+1) [(x+1)² + (x+1) - 2] + 1

f(x+1) = (x+1) [x² + 2x + 1 + x+1 - 2] + 1

f(x+1) = (x+1) [x² + 3x] + 1

f(x+1) = x³ + 3x² + x² + 3x + 1

f(x+1) = x³ + 4x² + 3x + 1.................ANS

Shifting, Reflecting and Stretching Graphs?

1. Match the following description of the transformation f(x) to the parent graph of g(x)= |x|.
1. f(x)=1/2 |x|
2. f(x)= - |x|
3. f(x)= |x - 2|
4. f(x)= |x| - 2
5. f(x) = |x|
6. f(x)= 2|x|

a. Horizontal shift right 2 units
b. Vertical Shift down 2 units
c. No Transformation
d. Vertical Stretch by a factor of 2
e. Reflection over the x axis
f. Vertical Shrink by a factor of 1/2

2. What affect does the constant have on the graph of f(x)= (x-3)^2?
Horizontal Shift Right 3
Horizontal Shift Left 3
Vertical Shift Up 3
Vertical Shift Down 3

3.What affect does the constant have on the graph of f(x)=(x-1)^2+2?
Vertical shift down 1 and horizontal shift right 2
Vertical shift up 1 and horizontal shift right 2
Vertical shift down 2 and horizontal shift left 1
Vertical shift up 1 and horizontal shift left 2
Vertical shift up 2 and horizontal shift left 1
Vertical shift up 2 and horizontal shift right 1

4. Given that the parent graph is f(x) describe the translation for 3f(x+3) - 4. (Hint: This could be any function)

6. What affect does the constant have on the graph of f(x)= x^2 + 3?
Vertical Shift Down 3
Horizontal Shift Right 3
Vertical Shift Up 3
Horizontal Shift Left 3

7. What affect does the constant have on the graph of f(x)= (x+3)^2?
Horizontal Shift Right 3
Horizontal Shift Left 3
Vertical Shift Down 3
Vertical Shift Up 3

8. Fill in the Blank
Givenf(x)=x^2 and g(x)= -x^2 the two functions are _____________ of each other.

9.Given that the parent graph is f(x) describe the translation for f(x)= - 1/4 (x)^2 + 3.

10. Given f(x) is the parent function describe what each variable means as a constant in terms of the translation for the graph. For example how does a affect the function. You should describe a,b, and c.

f(x) = a|x - b| + c

11. What affect does the constant have on the graph of f(x)= x^2 - 3?
Horizontal Shift Left 3
Vertical Shift Down 3
Vertical Shift Up 3
Horizontal Shift Right 3

Write the function whose graph is the graph of y=x^3, but is shifted to the right 2 units?

y = (x-h)^2 +k
h is shifting on the x axis and k is the shift on the y axis

The graph of y= - sqrt(x) is shifted 4 units up and 3 units right. What equation represents the new graph?

To get the graph 4 units up just add 4 to y.... To get the graph 3 units right just subtract 3 to x...

Then equation of the new graph is y = - sqrt(x-3) + 4 OK!

Functions and Their Graphs?

1. Use the graph of f(x) = x2 to match the function to its corresponding graph. In words describe the transformation that occurs (ex: The graph of f(x) is shifted 6 units to the left).
f(x) = x2
Choose from the following functions:
g(x) = (x – 2)2 ; h(x) = x2 – 2 ; i(x) = (x + 3)2 ; j(x) = (x + 1)2 + 3
a)
Function:
Description of transformation:
b)
Function:
Description of transformation:
c)
Function:
Description of transformation:
d)
Function:
Description of transformation:
2. Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations.
a) f(x) = 4x2 – 7x + 3
Show Work or Explain in Words:
b) g(x)=10/x+7
Show Work or Explain in Words:
c) f(x)=/4x-16
Show Work or Explain in Words:
d) g(x)=2x/x-3
Show Work or Explain in Words:
e) f(x) = 3x - 9
Show Work or Explain in Words:
3. Find the specified asymptotes of the following functions. Recall that asymptotes are lines therefore the answer must be given as an equation of a line.
a) Find the equation of the vertical asymptote of the function : f(x)=4/x+5
Show Work or Explain in Words:
b) Find the equation of the horizontal asymptote of the function: g(x)=5x^2-4/x+1
Show Work or Explain in Words:
c) Find the equations of both the vertical and horizontal asymptotes of the function: f(x)=3x-1/x+4