What is the affect on the graph of the linear parent function f(x) equals X when FX is replaced by FX +3
1 answer:
Answer:
The graph of the f(x) will horizontal shift left by 3 when f(x) is replaced by f(x+3).
Step-by-step explanation:
We know that when we add a constant to the input of the parent function, we get a horizontal shift.
The direction of shifting depends upon the value of the added constantly. If the added constant is negative, the shift of the graph will be left and if the added constant is positive, the shift of the graph will be right.
For example, consider the function
f(x)
so adding in the put i.e.
would be a change on the inside of the function, giving a horizontal shift left by 3.
Therefore, the graph of the f(x) will horizontal shift left by 3 when f(x) is replaced by f(x+3).
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Answer:
V = 1/6 cubic units
Step-by-step explanation:
Applying the concept of integrals for volume calculation:
(1)
V = volume of the solid bounded by x = a and x = b
S(x) = cross section area of the solid, perpendicular to the x axis
From the figure we have that S is the area of a triangle that has base Z and height Y
Area of the triangle = (2)
Calculation of y(x) and z(x)
We apply the equation of the point-slope line (plane xy):
Slope = (3)
Equation of the line = (4)
Replacing the points (1,0) and (0,1) in (3):
Replacing the point (1,0) and m = -1 in (4):
y(x) = -x + 1 (Line A-B) (5)
We apply the equation of the point-slope line (plane xz):
Slope = (6)
Equation of the line = (7)
Replacing the points (1,0) and (0,1) in (6):
Replacing the point (1,0) and m = -1 in (7):
z(x) = -x + 1 (Line A-C) (8)
Replacing (5) and (8) in (2)
(9)
Replacing (9) in (1) and knowing that a = 0 and b = 1:
evaluated from x=0 to x=1
