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Domain and Range of Functions>
Domain and Range of Functions 2Domain and Range of Functions 2
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Question 1 of 4
1. Question
Find the domain and range of `y=-1/x`
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The domain and range is the set of `x` and `y` values of a functionNotice that the curves extend infinitely on all sides but does not touch the `x` and `y` axis
This means that the curves will cover all real values of `x` not equal to `0` and all real values of `y` not equal to `0``\text(Domain: All real numbers)≠0``\text(Range: All real numbers)≠0` -
Question 2 of 4
2. Question
Find the domain and range of `y=4^x`
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The domain and range is the set of `x` and `y` values of a functionNotice that the curve extends infinitely on both sides of the x-axis. It also extends upward infinitely, but does not touch the x-axis
This means that the curve will cover all real values of `x` and all real values of `y` greater than `0``\text(Domain: All real numbers)``\text(Range): y>0` -
Question 3 of 4
3. Question
Find the domain and range`f(x)=3/(x-3)`Hint
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The domain and range is the set of `x` and `y` values of a functionRecall that fractions cannot have `0` as the denominator or the value will be undefined`f(x)` `=` `3/(x-3)` `f(3)` `=` `3/(3-3)` Substitute `x=3` `=` `3/0` `=` `\text(undefined)` Since `x=3` makes the denominator equal to `0`, $$x≠3$$Therefore, the domain is all real numbers $$≠3$$Next, recall that `f(x)=y` and `f(x)` cannot be equal to `0` since the equation will have no solution.Therefore, the range is all real numbers $$≠0$$`\text(Domain: All real numbers)` $$≠3$$`\text(Range: All real numbers)` $$≠0$$ -
Question 4 of 4
4. Question
Graph and find the domain and range`f(x)=(-5)/(x+1)`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` `-3` `-1` `-1/2` `0` `1` `3` `y` Substitute the values of `x` to the function to get their `y` values`x=-5``f(x)` `=` `(-5)/(x+1)` `f(-5)` `=` `(-5)/(-5+1)` Substitute `x=-5` `=` `-5/-4` `=` `1.3` Rounded to one decimal place `x=-3``f(x)` `=` `(-5)/(x+1)` `f(-3)` `=` `(-5)/(-3+1)` Substitute `x=-3` `=` `-5/-2` `=` `2.5` `x=-1``f(x)` `=` `(-5)/(x+1)` `f(-1)` `=` `(-5)/(-1+1)` Substitute `x=-1` `=` `-5/0` `=` `\text(undefined)` `x=-1/2``f(x)` `=` `(-5)/(x+1)` `f(-1/2)` `=` `(-5)/(-1/2+1)` Substitute `x=-1/2` `=` `-5/(1/2)` `=` `-10` `x=0``f(x)` `=` `(-5)/(x+1)` `f(0)` `=` `(-5)/(0+1)` Substitute `x=0` `=` `-5/1` `=` `-5` `x=1``f(x)` `=` `(-5)/(x+1)` `f(0)` `=` `(-5)/(1+1)` Substitute `x=1` `=` `-5/2` `=` `-2.5` `x=3``f(x)` `=` `(-5)/(x+1)` `f(0)` `=` `(-5)/(3+1)` Substitute `x=3` `=` `-5/4` `=` `-1.3` Rounded to one decimal place `x` `-5` `-3` `-1` `-1/2` `0` `1` `3` `y` `1.3` `2.5` `\text(und.)` `-10` `-5` `-2.5` `-1.3` Next, plot the points to the graph and connect them to form the curve.Recall that undefined values are asymptotes
Notice that the curves extend infinitely on all sides but do not touch the asymptote at `x=-1` and the x-axisThis means that the curves will cover all real values of `x` not equal to `-1` and all real values of `y` not equal to `0``\text(Domain: All real numbers)` $$≠-1$$`\text(Range: All real numbers)` $$≠0$$