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 please help. sorry this is so much! studying for my final.
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) Answer: Function: Description of transformation: b) Answer: Function: Description of transformation: c) Answer: Function: Description of transformation: d) Answer: 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 Answer: Show Work or Explain in Words: b) g(x)=10/x+7 Answer: Show Work or Explain in Words: c) f(x)=/4x-16 Answer: Show Work or Explain in Words: d) g(x)=2x/x-3 Answer: Show Work or Explain in Words: e) f(x) = 3x - 9 Answer: 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 Answer: Show Work or Explain in Words: b) Find the equation of the horizontal asymptote of the function: g(x)=5x^2-4/x+1 Answer: 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 Answer: Vertical: Horizontal: Show Work or Explain in Words: d) Find the equations of both the vertical and horizontal asymptotes of the function: g(x)=x+7/x^2-4 Answer: Vertical: Horizontal: Show Work or Explain in Words:
How would I transform the function y=2^x to obtain the graph of y=2^(x+1)-3?
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