Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?
2 answers:
Answer:
f(x) shift right 2 and up 3 to get g(x)
A is correct.
Step-by-step explanation:
Given: and
We need to find transformation that occurs from f(x) to g(x).
Parent function is quadratic equation.
Concept of transformation:-
For horizontal shift:
If x changes to x+a then left or right shift.
a>0 then shift left
a<0 then shift right
For vertical shift:
If y changes to y+a then up or down shift
If b>0 then shift up by a unit
If b<0 then shift down by a unit.
Thus, f(x) shift 2 unit right.
Thus, f(x) shift 3 unit up.
Hence, f(x) shift right 2 and up 3 to get g(x)
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Inequation 1:
to plot the pairs (x, y) for which the inequation holds, draw the line
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
draw the lines
i) use points (0, -3), (3, -1)
ii)
use points ( 0, 4), (3, 2)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
;
, not true so we color the region not containing this point
not true, so we color the region not containing the point (3, 3)
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.
to plot the pairs (x, y) for which the inequation holds, draw the line
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
draw the lines
i)
ii)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.