Generally a function is described in the form y = f(x), y being the value the function at any general point x in the domain of the function. The letter y is chosen because the values of the function is represented by the y-axis in a graph.
The graph of the function gives a visual presentation of the function which helps us to study the function at a glance.
The values of square root of positive real numbers is expressed as function f(x) = square root of x or simply y = square root of x. The graph of y = square root of x is an interesting study and let us take a closer look.
Concept of a Square Root Function:
Consider a simple square function y = x2. It is a special form of a quadratic function. We know that the graph of a quadratic function is a parabola. In this case it is a vertical, concave up parabola with origin as vertex. The graph is shown below.
Let see what is the inverse of the function y = x2
y = x2, or, √y = x and by interchanging the variable we get the inverse function as,
y = √x
Thus the square root function is nothing but the inverse of the square function.
We had seen that the graph of y = = x2 is symmetrical over y –axis. Therefore, the graph of y = square root of x has to be symmetrical over x-axis. However, since negative values of root of x have no meaning, the graph exists only in the first quadrant of the Cartesian system. It is shown below.
Example Problems on Graph of Y Square Root of X
From the graph of y square root of x, find the value of square root 3 to the nearest tenths. (Assume the sale to be 1unit on both the axes)
Since the scale of the graph is 1 unit each small division represents 0.2 unit. It is seen from the graph, when x = 5, the value of y is 1.7. Hence, square root of 3 is 1.7, nearest to tenths.
Use the graph of y square root of x, to evaluate 2( square root 6) to the nearest tenths. (Assume the sale to be 1unit on both the axes)
Since the scale of the graph is 1 unit each small division represents 0.2 unit. It is seen from the graph, when x = 6, the value of y is 2.5. Hence, 2(square root of 6) = 2(2.5) = 5
The graph of the function gives a visual presentation of the function which helps us to study the function at a glance.
The values of square root of positive real numbers is expressed as function f(x) = square root of x or simply y = square root of x. The graph of y = square root of x is an interesting study and let us take a closer look.
Concept of a Square Root Function:
Consider a simple square function y = x2. It is a special form of a quadratic function. We know that the graph of a quadratic function is a parabola. In this case it is a vertical, concave up parabola with origin as vertex. The graph is shown below.
Let see what is the inverse of the function y = x2
y = x2, or, √y = x and by interchanging the variable we get the inverse function as,
y = √x
Thus the square root function is nothing but the inverse of the square function.
We had seen that the graph of y = = x2 is symmetrical over y –axis. Therefore, the graph of y = square root of x has to be symmetrical over x-axis. However, since negative values of root of x have no meaning, the graph exists only in the first quadrant of the Cartesian system. It is shown below.
Example Problems on Graph of Y Square Root of X
From the graph of y square root of x, find the value of square root 3 to the nearest tenths. (Assume the sale to be 1unit on both the axes)
Since the scale of the graph is 1 unit each small division represents 0.2 unit. It is seen from the graph, when x = 5, the value of y is 1.7. Hence, square root of 3 is 1.7, nearest to tenths.
Use the graph of y square root of x, to evaluate 2( square root 6) to the nearest tenths. (Assume the sale to be 1unit on both the axes)
Since the scale of the graph is 1 unit each small division represents 0.2 unit. It is seen from the graph, when x = 6, the value of y is 2.5. Hence, 2(square root of 6) = 2(2.5) = 5
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