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Domain and Range of Functions>
Domain and Range of Functions 3Domain and Range of Functions 3
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Question 1 of 4
1. Question
Graph and find the domain and range`y=sqrt(x-5)`Hint
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The domain and range is the set of `x` and `y` values of a functionFirst, use a table of values and test several values of `x` to get the value of `y``x` `5` `6` `7` `9` `10` `y` Substitute the values of `x` to the function to get their `y` values`x=5``f(x)` `=` `sqrt(x-5)` `f(5)` `=` `sqrt(5-5)` Substitute `x=5` `=` `sqrt0` `=` `0` `x=6``f(x)` `=` `sqrt(x-5)` `f(6)` `=` `sqrt(6-5)` Substitute `x=6` `=` `sqrt1` `=` `1` `x=7``f(x)` `=` `sqrt(x-5)` `f(7)` `=` `sqrt(7-5)` Substitute `x=7` `=` `sqrt2` `x=9``f(x)` `=` `sqrt(x-5)` `f(9)` `=` `sqrt(9-5)` Substitute `x=9` `=` `sqrt4` `=` `2` `x=10``f(x)` `=` `sqrt(x-5)` `f(10)` `=` `sqrt(10-5)` Substitute `x=10` `=` `sqrt5` `x` `5` `6` `7` `9` `10` `y` `0` `1` `sqrt2` `2` `sqrt5` Next, plot the points to the graph and connect them to form the curve.
Notice that the curve Starts at the point `(5,0)` and extends infinitely to the right sideThis means that the curves will cover all real values of `x` greater than or equal to `5` and all real values of `y` greater than or equal to `0``\text(Domain:) x≥5``\text(Range:) y≥0` -
Question 2 of 4
2. Question
Find the domain`y=3/(2x-1)`Hint
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The domain and range is the set of `x` and `y` values of a functionFor finding the domain, focus on the value of the denominatorRecall that fractions cannot have `0` as the denominator or the value will be undefined`2x-1` `≠` `0` `2x-1` `+1` `≠` `0` `+1` Add `1` to both sides `2x``divide2` `≠` `1``divide2` Divide both sides by `2` `x` `≠` `1/2` Since `x=1/2` makes the denominator equal to `0`, $$x≠\frac{1}{2}$$Therefore, the domain is all real numbers $$≠\frac{1}{2}$$`\text(Domain: All real numbers)≠1/2` -
Question 3 of 4
3. Question
Find the domain`y=1/(sqrt(2x-3))`Hint
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The domain and range is the set of `x` and `y` values of a functionFor finding the domain, focus on the value of the denominatorRecall that fractions cannot have `0` as the denominator or the value will be undefined. Also, since the value of the denominator is a square root, it cannot have a negative value.`2x-3` `>` `0` `2x-1` `+3` `>` `0` `+3` Add `3` to both sides `2x``divide2` `>` `3``divide2` Divide both sides by `2` `x` `>` `3/2` Therefore, the domain is all real numbers greater than `3/2``\text(Domain):x>3/2` -
Question 4 of 4
4. Question
Find the domain`y=3/(sqrt(3-4x))`Hint
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The domain and range is the set of `x` and `y` values of a functionFor finding the domain, focus on the value of the denominatorRecall that fractions cannot have `0` as the denominator or the value will be undefined. Also, since the value of the denominator is a square root, it cannot have a negative value.`3-4x` `>` `0` `3-4x` `-3` `>` `0` `-3` Subtract `3` from both sides `-4x``divide(-4)` `>` `-3``divide(-4)` Divide both sides by `-4` `x` `<` `3/4` Flip the inequality Therefore, the domain is all real numbers less than `3/4``\text(Domain):x<3/4`