If f(x) = x^2 - 4x + 1, find the range of f(x). {y: y ≥ -3} {y: y ≥ 13} all reals
1 answer:
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Answer:
Area of ΔPQR is 28 units²
Step-by-step explanation:
-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point P( 0, b)
x-2y+2 = 0, subtract x and 2 from both sides
-2y = -x-2, divide by -2 both sides
y= (1/2)x +1 so b=1 and P (0, 1)
-Q is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point Q( 0, b)
3x +y -15 =0, subtract 3x and add 15 to both sides
y= -3x +15 so b=15 and Q(0,15)
-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15
(1/2)x +1 = -3x +15, add 3x and subtract1
(1/2) x+3x = 15-1, combine like terms
(7/2)x = 14 , multiply both sides by 2
7x = 28, divide both sides by 7
x= 4
y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)
- the area of ΔPQR is (base *height)/2
base= 15-1= 14
height = 4
A= (14*4)/2 = 14*2 = 28
Given:
The function is:
The function f(x) is multiplied by a factor of 2 and then 3 is added to the function.
To find:
The effect on the graph of the function.
Solution:
The transformation is defined as
.... (i)
Where, k is stretch factor and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
It is given that the function f(x) is multiplied by a factor of 2 and then 3 is added to the function. So, the new function is:
...(ii)
On comparing (i) and (ii), we get
, it means the graph is vertically stretched by a factor of 2.
, it means the graph is shifted up 3 units.
Therefore, the correct option is D.