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Graph each generalized square root function. Give the domain and range. See Examples 4 and 5.$$\frac{y}{2}=\sqrt{1+\frac{x^{2}}{4}}$$
Precalculus
Algebra
Chapter 13
Nonlinear Functions, Conic Sections, and Nonlinear Systems
Section 3
The Hyperbola and Functions Defined by Radicals
Introduction to Conic Sections
An Introduction to Geometry
Functions
Systems of Equations and Inequalities
Missouri State University
Campbell University
Oregon State University
University of Michigan - Ann Arbor
Lectures
01:32
In mathematics, the absolu…
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Graph each generalized squ…
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Graph each equation. Give …
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04:32
Graph each function. State…
So this problem we have why over two is equal to the square root of one plus X squared over four. Since you have addition under the radical we know we're gonna be looking at half of a hyper Bella. And in this case, because it's positive we're looking at the top half of the hyperbole. Well, let's clean this up so we can see exactly where this will fall. Squaring both sides. We get why squared over four is equal to one plus X squared over four. Moving the X squared over four to the other side. We're gonna get our standard form of a higher purple. Since nothing is being added, subtracted to the numerator is my center still at 00 in this case, I'm going to go up two units to get to the verge. ISI, I'm not gonna go down two units because it's only half of it, and I'm only focusing on the positive part. I'm gonna go right and left two units help me to create my part of my rectangle. So I know how wide my hyperbole a should be. Remember, the Assam toes travel from the center through the vergis ease of the rectangle. My picture goes through the vergis ease and snuggles up to the aspen totes. So this is what my picture looks like. Therefore, my domain are the X values from negative infinity to positive infinity in the range or my Y values from positive to inclusive, up to positive infinity.
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