#Piecewise function graphs plus#

Include the endpoints of the interval without fail.

Make a table with two columns labeled x and y corresponding to each interval.

Write the intervals that are shown in the definition of the function along with their definitions.

For example, f(x) = ax + b represents a linear function (which gives a line), f(x) = ax 2 + bx + c represents a quadratic function (which gives a parabola), etc, so that we will have an idea of what shape the piece of the function would result in.

First, understand what each definition of the function represents.

Here are the steps to graph a piecewise function. That has been defined in a piecewise way.We already know that the graph of a piecewise function has multiple pieces where each piece corresponds to its definition over an interval. And so this one actuallyДoesn't have any jumps in it. So when x is equal to 10, our function is equal to negative six. That is negative 66 over 11, which is equal to negative six. Over 11, is that right? Let's see, if you, yeah, This is going to be, what is this? This is negative 66 I just multiplied this times 10, 12 times 10 is 120, and In that right over there, and then when x is equal to 10, you have negative 120 over 11. Is equal to 66 over 11 which is equal to positive six.

#Piecewise function graphs plus#

It by negative one, plus 54 over 11 which To be positive 12 over 11 'cause we're multiplying When x is negative one, you're going to have, well, this is just going And now let's look at this last interval. So, that's that interval right over there. One, we're approaching negative one plus seven is six.

We are approaching, or as x approaches negative Including x equals negative one up to and including, so it's So we're actually able to fill it in, and then when x is negative one, negative one plus seven is Negative two comma five, so it actually includes Two, when x equals negative two negative two plus seven is, The next interval, this one'sДЄ lot more straightforward. I am going to draw my bestДЄttempt, my best attempt, at the line. Little open circle there, and then I'm gonna draw the line. We might be tempted, to just circle in this dot over here, but remember, this intervalДoes not include negative two. Two, we have negative 0.125 times negative two plus 4.75 is equal to, see negative times negative is positive, two times this is going to be point, is going to be positive 0.25 plus 4.75. Includes, so x is defined there, it's less than or equal to, and then we go all the Negative is a positive, and then 10 times this is That is going to be equal to, let's see, the negative times a Let me do it over here where I do the, so we're going to have negative 0.125 times negative 10 plus 4.75. Negative 10, so we would have negative zero, actually So, when x is equal to 10, sorry, when x is equal to Think about graphing it is let's just plot the endpoints Line, a downward sloping line, and the easiest way I can Less than or equal to x, which is less than negative two, then our function is definedД«y negative 0.125x plus 4.75. So, let's think about this first interval. This on your own first before I work through it. If you have some graph paper, to see if you can graph Over this interval for x, this line over this interval of x, and this line over this interval of x. You see this right over here,Д®ven with all the decimals and the negative signs, It's defined as a different,Д®ssentially different lines. Have this somewhat hairy function definition here, and I want to see if we can graph it.