Given f(x) = x2 - 10x + 22, what is the domain of f

1 answer:

4 0

<h2><u>Answer:</u></h2><h2>Polynomials have the domain of all Reals. Plugging any Real number into the equation will give you a value. </h2><h2>Domain = {x|x∈R}</h2><h2><u></u></h2><h2><u> Step-by-step explanation:</u></h2><h2>The range is dependent on the curve itself. The axis of symmetry for this function is</h2><h2>x = -b/2a = -1(-10)/2(1) = 10/2 = 5 </h2><h2>The vertex is F(5) = (5)2 + (-10)(5) + 21 = 21 -50 + 21 = -8</h2><h2>Since the leading coefficient is positive, the parabola opens up and the vertex (5,-8) is a local minimum. It turns out to be an absolute minimum too so the Range = {x|x∈R, x≥-8}</h2>

<h2><u>Thank you</u></h2><h2><u>sunshinemadison101</u></h2>

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Which statements about the system are true?

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2 Answers:

B) The lines are parallel
C) The lines have the same slope.

Parallel lines always have equal slope, but different y intercepts.

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Explanation:

Let's solve the second equation for y

3y - x = -7

3y = -7+x

3y = x-7

y = (x-7)/3

y = x/3 - 7/3

y = (1/3)x - 7/3

The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.

However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.

Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.

Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.

I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.