question 6 5 points graph the function fx begincases 2 textfor x ge 1 3 x textfor x 1 endcases 3

Step 1: First, we need to graph the function for $x ge 1$. Since $f(x) = 2$ for $x ge 1$, we

Question 6 5 points graph the function fx begincases 2...

Transcript

00:02 In this problem, we are going to graph the piecewise function named f of x.

00:09 So there's two pieces to this function.

00:12 One of them, the equation is 2x plus 3 when our x values are less than 0.

00:18 So on this side of the y -axis, x is less than 0.

00:24 And then our other function is 3 minus x when x is greater than are equal to 0 on this side of the y -axis and at the y -axis.

00:32 We'll look at that.

00:34 I'm first going to grab a yellow, and i'm going to graph y equals 2x plus 3.

00:42 We know that that is in a slope intercept form.

00:46 We would have a point at 3 and a slope of up 2 over 1.

00:51 Okay? so we know besides up 2 over 1, we can go down to backwards 1.

00:58 And that would be, we would draw our line through that if we were graphing the whole equation, and y equals 2 x plus 3 but we all we just want part of it we want when x is less than 0 so this point is not part of our domain so we're going to get rid of it and also we want when x is less than 0 so when x equals 0 we're at that point 03 we don't want that point but we want everything to the left of it so i'm going to erase that point as well and we're going to put an open circle there because we want everything right up to that but not that exact point.

01:41 So this part of our graph, this piece of our graph is this.

01:47 Okay, so this one is graph correctly now in orange...

Question

Question 6 (5 points) Graph the function. $$f(x) = \begin{cases} 2 & \text{for } x \ge 1 \\ -3-x & \text{for } x < 1 \end{cases}$$

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