Difference between revisions of "Math 22 Functions"
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!Solution: | !Solution: | ||
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| − | |The domain is where the function defines. So, the radicand (everything under the square root) need to be non-negative. | + | |The domain is where the function defines (or all possible values of x). So, the radicand (everything under the square root) need to be non-negative. |
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|So, <math>x+1\geq 0</math> | |So, <math>x+1\geq 0</math> | ||
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|'''Answer''': <math>y\geq 0</math> | |'''Answer''': <math>y\geq 0</math> | ||
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==Notes:== | ==Notes:== | ||
Revision as of 09:21, 12 July 2020
Basic Definitions
A function is a relationship between two variables such that to each value of the independent variable there corresponds exactly one value of the dependent variable.
The domain of the function is the set of all values of the independent variable for which the function is defined. The range of the function is the set of all values taken on by the dependent variable.
Exercises Find the domain and range of the following functions:
1) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=\sqrt{x+1}}
| Solution: |
|---|
| The domain is where the function defines (or all possible values of x). So, the radicand (everything under the square root) need to be non-negative. |
| So, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x+1\geq 0} |
| Answer: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x\geq -1} |
| The range is all of possible outcomes (values of y). So, notice that Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{x+1}} is never negative. So Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} is never negative. |
| Answer: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y\geq 0} |
Notes:
This page were made by Tri Phan