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(a) determine the domain, (b) sketch the graph and (c) determine the range of the function defined by the given equation.$h(x)=\sqrt{x}$

(a) $x \geq 0$(b)(c) $y \geq 0$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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(a) determine the domain, …

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(a) identify the domain an…

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for this problem. We've been given a function. H h of X equals the square root of X, and we want to find three things. We would like to find the domain and range of our function H and then we're going to sketch it. Often. Seeing a visual representation of the function helps us determine that we have the correct domain in range. So domain range and our sketch. First, let's start with domain Domain is your input. That's all of the values of X that can go into your function often when we're doing domain. Instead of trying to figure out which X is we can use, it's helpful to think of which X is we can't use now. In this particular function, we do have a limitation. We have a square root we have toe have whatever's under the square root. In this case, X has to be non negative, so X has to be greater than or equal to zero. If X is negative, square it of a negative number that's no longer a real number that becomes imaginary, and we're looking just a real numbers here. So Doma domain is X is greater than or equal to zero. If we want to write this an interval notation, we could write this as 02 Infinity. We went with the bracket by the zero because zero is included. I can have X equals zero. That's valid and it increases. Okay, How about range? Range? Are your outputs your Why values? So for this function again, I have a square root square Roots always return positive numbers. Now, if x zero why could be zero? And then why is going to be positive? So no negative numbers allowed. So my range for why is my Y values is exactly the same as my domain. X has to be greater than or equal to zero. Why is going to be greater than or equal to zero? So let's plot some points. I know that 00 is on my graph spirit of zero is zero. And since Onley have positive numbers for X and Y, I'm only going to be in the first quadrant. Let's plant a couple of points and see what we get. Let's let X equal one. Well, the square root of one is one square root of four is too scared of nine is 356789123 So you can see I've got a gradually yeah, right. It's an increasing slope, but it's a very, very shallow slope in. The farther I go, it's gonna stay shallow, shallow, shallow all the way out. But I can have any extra wife. I make my graft big enough. I could eventually get to any extra why that I want to have but again, nothing in the other quadrants, because I can only have positive exes and positive wise. So this is my domain range and sketch from my function H of X.

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