Graph the equation by substituting and plotting points. Then reflect the graph across the line y

Graph the equation by substituting and plotting points. Then...

Key Concepts

Graphing by Substitution

This concept involves selecting a set of values for one variable, substituting these values into the equation, and then calculating the corresponding values for the other variable. Plotting these (x, y) pairs on the coordinate system helps to visually represent the behavior and shape of the graph. This method is particularly useful for understanding the relationships between variables and the overall structure of the graph.

Reflection Across the Line y=x

Reflecting a graph across the line y=x involves swapping the x and y coordinates of every point on the graph. This geometric transformation is essential when determining the graph of an inverse function, as the inverse essentially reverses the roles of the input and output. The process emphasizes the symmetry inherent in inverse relationships between functions.

Inverse Functions

An inverse function reverses the process of the original function by swapping the roles of the input and output. Graphically, the inverse is obtained by reflecting the original function's graph across the line y=x. Understanding inverse functions is crucial for solving equations, modeling relationships, and analyzing how changing one variable affects another.

Transcript

00:01 Equation x is equal to y square minus 3 first of all we'll draw a table and in that table we'll substitute some values of y and for that value of y what can be the value of x so first okay so we draw the table now i'm writing here x and here y so now i will take any random value which way which may be integers so i will take some integral value of y and for which i will see according to the given equation this what can be the value of x so if i take y is equal to so x will be minus 3 again i'm taking y is equal to minus 1 so if i take y is equal to minus 1 this will become 1 minus 3 that is minus 2 or if i take y is equal to 1 in that case also it will be minus 2 and if y is equal to minus 2 then x is equal to this is 2 minus 2 is 4 minus 3 is 1 again y is 2 then also it is 1 if y is 3 then this is 6 and y is so why is minus 3 then 6 why is 3 then also it is 6 now we'll see all these we will plot all these points on the graph so what are the coordinates of the point so we have minus 3 comma 0 minus 2 comma minus 1 minus 2 comma 1 1 comma minus 2 1 comma minus 2 1 comma 2 6 comma minus 3 and 6 comma 3 these are the points which which we have to plot on the graph so we can see so if this is origin so i'm taking here one two three four five six and this side also i'm taking minus one minus two minus three minus four above also one two three four five and six below it is minus one minus one minus two minus now first point is minus 3 x is minus 3 and y is 0.

02:33 So this is the point.

02:35 Next x is minus 2 and y is minus 1.

02:39 This is another point.

02:41 Again x is minus 2 and y is plus 1.

02:45 X is 1 and y is so x is 1, y is minus 2 so this is the point again x is 1 and y is plus 2 so this is another point x is minus x is 6 and y's minus minus 3 x is 6 and y is plus 3 so this is a parabola and the graph of this will be like this it is passing it cuts x xx is at minus 3 .0 now this is the given this is the graph of the given curve or the given equation now we have to draw the graph of y is equal to x so let us suppose that this is the graph of what we can see here this is the graph of y is equal to x now to get the graph of the function which is just inverse of the given curve what we need to do we'll take just reverse of this and we will take just the graph or the graph of the curve which reflect about this line which is y is equal to x so we will take now it was minus 3 .0 so here we will take 0.

04:13 Minus 3 and so on...

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