Question

g(x) is an even function. Does knowing that I'm x→7−g(x) = 2 tell you anything about lim x→−7−g(x)? What about lim x→−7+g(x)? Support your reasoning using the definition of an even function and a neat hand-drawn figure.

Answer 1

By definition, a function is even if:

f(x) = f(-x)

For every value of x.

With this, we will find:

$\lim_{x \to -7}-g(x) = 2\\\\\lim_{x \to -7} g(x) = -2$

Let's see how we got this:

Now that we know this, knowing that:

g(x) is even

$\lim_{x \to 7}-g(x) = 2$

From the above limit we can conclude that -g(7) ≈ 2

Then using the even property of g(x) is easy to see that:

$\lim_{x \to -7}-g(x) = 2\\\\\lim_{x \to -7} g(x) = -2$

Because we also should have -g(-7) = -g(7) ≈ 2

If you want to learn more, you can read:

brainly.com/question/16941091