The slope of the line is -3/4, so the answer is B
10x^3 is the greatest common factor
The transformations are vertical translation 7 units up.horizontal translation 3 units to the left
We have given that the equations
let f(x)=x^2 and g(x)=(x-3)^2+7
We have to determine the correct transformation,
<h3>What is the vertical translation?</h3>
Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated to k units vertically by moving each point on the graph k units vertically.
Notice that the addition of 2 units to the variable x in the exponent involves a horizontal shift to the left in 2 units.
Notice as well that subtraction of 4 units to the functional expression involves a vertical shift downwards in 4 units.
To learn more about the transformation visit:
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Short Answer A
Comment
It's a good thing that the domain is confined or the graph is. That function is undefined if x < - 3
At exactly x = - 3, f(x) = 0 and that's your starting point.
So look what happens to this graph. If x = 0, f(0) = y = 3. So we are starting to see that as x get's larger so does f(x). The graph tells us that x = 0 is bigger than x = - 3.
Let's keep on plugging things in.
As x increases to 5, f(5) = 5. x = 5 is larger than x = 0, and f(5) > 3.
One more and then we'll start drawing conclusions. If x = 9 then f(9) = y = 6.
x = 9 is larger than x = 5. f(9) = 6 is just larger than f(5) which is 5
OK I think we should be ready to look at answers. There's nothing there that makes the answer anything but a. Let's find out what the problem is with the rest of the choices.
B
The problem with B is that as x increases, f(x) does not decrease. We didn't find one example of that. So B is wrong.
C
C has exactly the same problem as B.
D
The second statement in D is incorrect. As x increases f(x) never decreases. No example showed that.
The answer is A <<<< Answer.
