Square Root Graph: Understanding x- & y- Intercepts

In summary, the graph of the function y=\sqrt{x}-4 will only be in the first quadrant due to the restriction of a function. This means it will not extend to the negative x-axis. The choice of the positive square root is a convention to ensure the graph is a function. Other graphs, such as a sideways parabola or a circle, are not functions but can still be plotted.
  • #36
lLovePhysics said:
What's so important about functions anyways? All they have are two y outputs for every x input right? Would it make a big difference (and get marked wrong) if I drew a horizontal parabola rather than just the top half??
No, they have one y output for every x input! If you were specifically asked to graph the function [itex]y= \sqrt{x}[/itex] and graphed the entire parabola, yes you would be marked wrong. If you were asked to graph x= y2 (so y is a "relation", not a function of x, though now x is a function of y) then you should graph the entire parabola.

There is nothing terribly important about "functions" (except that they are somewhat simpler than "relations") in mathematics but they tend to be very important in applications of mathematics to science because of the requirement of "repeatability": if you do an experiment twice, with everything set up exactly the same way, you should get exactly the same result- one input, one output. "This causes that" gives functions.

Think of it this way: If you were to go to a store and find different products that had the same price, you would not be surprised, right? The "product" is not a function of the price. On the other hand, if you found exactly the same product, same size, brand, and everything, in the same store for two different prices, you would know that something was wrong: the price is a function of the product.
 
<h2>1. What is a square root graph?</h2><p>A square root graph is a type of graph that represents the square root function, which is a mathematical function that takes the square root of a number. The graph is a curved line that starts at the origin and increases as the input value increases.</p><h2>2. How do you plot a square root graph?</h2><p>To plot a square root graph, you need to choose a set of input values, also known as x-values, and calculate the corresponding output values, or y-values, by taking the square root of each x-value. Then, plot the points on a coordinate plane and connect them with a smooth curve to create the graph.</p><h2>3. What are the x- and y-intercepts of a square root graph?</h2><p>The x-intercept of a square root graph is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis. For a square root graph, the x-intercept is always at the origin (0,0), and the y-intercept is undefined.</p><h2>4. How do you find the domain and range of a square root graph?</h2><p>The domain of a square root graph is all the possible input values, or x-values, that can be used to calculate the output values, or y-values. In other words, the domain is all real numbers greater than or equal to 0, since you cannot take the square root of a negative number. The range of a square root graph is all the possible output values, or y-values, which is also all real numbers greater than or equal to 0.</p><h2>5. How can you use a square root graph to solve real-life problems?</h2><p>Square root graphs can be used to solve real-life problems that involve finding the length of a side of a square or rectangle, the distance between two points, or the velocity of an object in free fall. By understanding the x- and y-intercepts of the graph, you can determine the values of the variables in the problem and solve for the unknown quantity.</p>

1. What is a square root graph?

A square root graph is a type of graph that represents the square root function, which is a mathematical function that takes the square root of a number. The graph is a curved line that starts at the origin and increases as the input value increases.

2. How do you plot a square root graph?

To plot a square root graph, you need to choose a set of input values, also known as x-values, and calculate the corresponding output values, or y-values, by taking the square root of each x-value. Then, plot the points on a coordinate plane and connect them with a smooth curve to create the graph.

3. What are the x- and y-intercepts of a square root graph?

The x-intercept of a square root graph is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis. For a square root graph, the x-intercept is always at the origin (0,0), and the y-intercept is undefined.

4. How do you find the domain and range of a square root graph?

The domain of a square root graph is all the possible input values, or x-values, that can be used to calculate the output values, or y-values. In other words, the domain is all real numbers greater than or equal to 0, since you cannot take the square root of a negative number. The range of a square root graph is all the possible output values, or y-values, which is also all real numbers greater than or equal to 0.

5. How can you use a square root graph to solve real-life problems?

Square root graphs can be used to solve real-life problems that involve finding the length of a side of a square or rectangle, the distance between two points, or the velocity of an object in free fall. By understanding the x- and y-intercepts of the graph, you can determine the values of the variables in the problem and solve for the unknown quantity.

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