This is the graph of y or f of x is equal to two times the absolute value of x plus three, plus two. This is going to be shifted. Or essentially multiply the slope by two. And then that last piece, says shift up by two.

Let me draw that right over there. So for x less than negative three, it'll look like that. So this is gonna be shifted up by two. If you're seeing this message, it means we're having trouble loading external resources on our website. When whatever we have inside the absolute value sign is positive, we're going to get essentially, this slope of one.

Video transcript - [Instructor] So we're asked to graph f of x is equal to two times the absolute value of x plus three, plus two.

Below x equals negative three, for x values less than negative three, what we're gonna have here, is this inside of the absolute value sign, is going to be negative and so then we're gonna take it's opposite value and so that makes sense. Y is equal is to the absolute value of x plus three.

So let me put that there. Absolute Value Functions An absolute value function is a function that contains an algebraic expression within absolute value symbols. And what they've already graphed for us, this right over here, this is the graph of y is equal to the absolute value of x.

So that is the graph of y is equal to two times the absolute value of x plus three. Now let's see if we can graph y is equal to two times the absolute value of x plus three. Main content. The vertex of the graph is h , k.

And so it's going to look... So if we shift three to the left, it's gonna look something like... Now for x is greater than negative three, when you add three to it, you're gonna get a positive value and so that's why you have this upward sloping line right over here.

That's why you have this downward line right over here.

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