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Given Y=\sqrt{x^2 + x - 2} Find the: a. domain b. x and y intercepts c. limits d. asymptotes e....

Question:

Given {eq}Y=\sqrt{x^2 + x - 2} {/eq}

Find the:

a. domain

b. x and y intercepts

c. limits

d. asymptotes

e. first derivative with increasing and decreasing lines

f. second derivative with up/down concavity and inflection points

g. graph

Radical Function at {eq}\mathbb{R} {/eq}:

To determine the graph of a radical function, we must know:

1) Domain.

2) {eq}x {/eq} and {eq}y- {/eq}intercept.

3) Critical point.

4) Asymptotes

5) Intervals of increase and decrease.

6) Concavity intervals and

7) Inflection point, among others.

Answer and Explanation: 1

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Let {eq}y= f(x)= \sqrt{x^2 + x-2} {/eq}.


a) Domain {eq}f. {/eq}

{eq}x^2 + x-2 \geq 0 \implies (x+2)(x-1) \geq 0. {/eq}


We must study two...

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What is a Radical Function? - Definition, Equations & Graphs

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Chapter 7 / Lesson 3
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Learn about how to find the domain of a radical function. Read about graphing radical functions, the domain of radical function, and radical function equations.

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