Which equals the product of (x – 3)(2x + 1)? 2x² – 7x-3 2x² – 5x-3 3x-2 0 6x²
1 answer:
You might be interested in
Answer:
7) K'(1, 1), N'(4, 0), Q'(4, 4)
9) F'(4, 2), W'(4, 5), K'(3, 2)
Step-by-step explanation:
When you are not sure about reflections and rotations, it can be useful to actually draw a graph. The line of reflection is the perpendicular bisector of the segment connecting a point with its image. That is, the image is the same distance from the line on the other side. A point that is <em>on</em> the line of reflection is "invariant," it doesn't move.
__
7) Reflecting across the x-axis changes the sign of the y-coordinate. That is all. Any point on the x-axis (y=0) is unchanged. The transformation is ...
(x, y) ⇒ (x, -y)
__
9) Reflecting across a vertical line changes the x-coordinate. The new value of x will be ...
x' = 6 - x
The "6" is double the x-coordinate of the vertical line. The transformation is ...
(x, y) ⇒ (6-x, y)
_____
<em>Derivation of the formula for reflection on x=3</em>
In general if M is the midpoint of a point (A) and its reflection (A'), then we have ...
M = (A +A')/2
2M = A + A'
2M -A = A'
When a point is reflected across a vertical line, all of the y-coordinate values remain unchanged. So, for A=(x, y) and M=(3, y), we have ...
A' = 2(3, y) -(x, y) = (6-x, 2y-y)
A' = (6 -x, y)
So, the reflection transformation across the line x = 3 is ...
(x, y) ⇒ (6-x, y)
Answer:
f(x) = -2x + 7, when x > 1
f(x) = 4x + 1 when x ≤ 1
Step-by-step explanation:
The right side graph passe through points (1,5) and (2,3).
Hence, the equation of the line
⇒ (y - 5) = 2(1 - x)
⇒ y - 5 = 2 - 2x
⇒ y = -2x +7.......... (1)
Now, the left side graph passes through points (1,5) and (0,1)
Therefore, the equation of the graph will be
⇒ y - 5 = 4(x - 1)
⇒ y = 4x + 1 ........ (2)
Hence, the equation (1) gives the function in the right side of the given graph which does not include the point (1,5) and extends to the right from this point.
Therefore, f(x) = -2x + 7, when x > 1 (Answer)
Again, equation (2) gives the function in the left side of the given graph which includes the point (1,5) and extends to the left from this point.
Therefore, f(x) = 4x + 1 when x ≤ 1 (Answer)