For each equation, (a) give a table with at least three ordered p...

Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.

y = √x - 3

Accepted Answer

Hey, everyone. Here we are asked for the following equation sketch its graph by using a table of ordered pairs. Here we are given the equation Y is equal to negative seven plus the square root of X. Now to begin this problem, we want to start by looking at our given equation. And here we want to notice that we have the square root of X. So that tells us that we cannot have a negative value for X or that X must be greater than or equal to zero. And this tells us that our curve will look like half of a Parabola which opens to the right or a Parabola which lies on its side. So now we want to start finding relevant points so we can begin by finding our X value for when Y is equal to zero. So substituting zero into our equation, we have zero is equal to negative seven plus the square root of X. Now just solving for X, we want to add seven to both sides. So we have the square root of X is equal to seven. Now getting rid of the square root, we have to raise both sides of the equation to the power of two. And so we find that X is equal to 49. So with this, we can begin our table of values. So we have one column for the X values and the other column for the Y values. And here we have found that when Y is zero, X is 49 and now we can move on to finding more points. So the next significant point is when X is equal to zero. And so finding this value for Y, we have Y is equal to negative seven plus the square root of zero. And now just simplifying, we find Y is equal to negative seven. Now going back to our table of values, we see that when X is zero Y is negative seven and now we just want to find one more point. So let's say we want to find the value of Y when X is equal to 100. And so now solving our equation, we have Y is equal to negative seven plus the square root of 100. And now just simplifying we have Y is equal to negative seven plus 10. Some mean our values we have Y is equal to three. So now we have found and referring back to our table of values, we found that when X is equal to 100 that Y is equal to three. And now we just want to start sketching the graph. So we want to begin by plotting the points that we found. So starting with our first ordered pair, which is 49 and zero, we need to plot this point. So we plot 49 and zero. And now we can move on to the next ordered pair which is zero and negative seven. Next, we move on to our third point which is at positive three along the y axis. And so now we have plotted our three points. So all that is left to do is sketch the curve which intersects each of these points. So starting at our point that is on the Y axis, we then go through our other two points and we draw an arrow at the end of the curve to represent our line extending to infinity. And with this, we have sketched the graph of our given equation. And so we are done solving this problem. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4. y = √x - 3

Key Concepts

Ordered Pairs

Graphing Functions

Square Root Function

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