Answer:
One solution (-1,2)
Step-by-step explanation:
Since these two linear equations have different slopes, different y-intercepts, and are indeed linear, these equations will only have one crossing when graphed, and hence one solution.
To find that solution, we can simply set the equations equal to each other.
y = -x + 1
y = 2x + 4
-x + 1 = 2x + 4
-3 = 3x
-1 = x
Now plug that value back into one of the equations:
y = -x + 1
y = -(-1) + 1
y = 2
So now you know the crossing for these two equations occurs at (-1,2).
Cheers.
F(x) is a parabola opening upward, while g(x) is a parabola facing downward.
So there needs to be a negative out front of the f(x) term. The negative will flip the parabola. That means the answer is either A or B
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After we flip the parabola, we need to translate the vertex (0,0) to the point (2,1) so that it matches up with the vertex of g(x)
To move from (0,0) to (2,1) we shift 2 units to the right and 1 unit up.
To move 2 units to the right, replace 'x' with 'x-2'
To move 1 unit up, you tack on a "+1"
So f(x) turns into -f(x) and then we replace the x with x-2 to get -f(x-2). Finally we tack on a "+1" to get -f(x-2)+1
The g(x) function is g(x) = -f(x-2)+1
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Therefore the final answer is choice B
Answer:
D.
Step-by-step explanation:
I am assuming they are not allowing graphing calculators for this, which is kind of wacky, if you ask me.
Anyway, the greater or equal to can technically be used interchangeably, so it looks like this:
y > 2x --> y = 2x
And so, with that equation, the sign just tells you what section of the graph is included. In this case, everything above the line.