Consider the function given by the graph. What are these values?

Mathematics

2 answers:

Natalija [7]3 years ago

5 0

As you see in the picture, there are two lines that could maybe represent two linear functions. However, this is not true because of the solid point and the hollow point. This is an inequality equation that has points of discontinuity.

Points of discontinuity are breaks in the graph that are a result of an undefined point when the f(x) is substituted with a point of x that is not part of the solution. So, technically, the graph is made from one rational expression.

So, when it says f(-2), this is the y-value at x=-2. That means f(-2)=2, f(0)=3 and f(4)=-1. Specifically, there are two points at x=0, but we take the solid point only.

Travka [436]3 years ago

5 0

Answer:

F(-2) = 2

F(0)= 3

F(4)= -1

Step-by-step explanation

Just took test

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Likurg_2 [28]

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Step-by-step explanation:

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2 years ago

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How to evaluate the limit

anzhelika [568]

$\displaystyle\lim_{x\to2}\frac{x^2-x+6}{x+2}$

Both the numerator and denominator are continuous at $x=2$ , which means the quotient rule for limits applies:

$\dfrac{\displaystyle\lim_{x\to2}(x^2-x+6)}{\displaystyle\lim_{x\to2}(x+2)}=\dfrac{2^2-2+6}{2+2}=\dfrac84=2$

Perhaps you meant to write that $x\to-2$ instead? In that case, you would have

$\displaystyle\lim_{x\to-2}\frac{x^2-x+6}{x+2}=\lim_{x\to-2}\frac{(x+2)(x-3)}{x+2}=\lim_{x\to-2}(x-3)=-2-3=-5$