Question

The function h is defined as follows for the domain given. h(x)= 1-2x, domain {-3,-2,1,5} Write the range of h using set notation. Then graph h .

Answer 1

`\lbrace7,6,-1,-9\rbrace`

Step-by-step explanation

`h\mleft(x\mright)=1-2x`
`Domain\text{ .}\lbrace-3,-2,1,5\rbrace`

Step 1

a)The domain of a function is the set of its possible inputs and the range of a function is the complete set of all possible resulting values of the dependent variable (y, usually)

so, to find the range input each value from the domain to obtain its image

so

`\begin{gathered} h\mleft(x\mright)=1-2x \\ hence \\ h\mleft(-3\mright)=1-2\left(-3\right)=1+6=7 \\ h\mleft(-2\mright)=1-2(-2)=1+4=5 \\ h\mleft(1\mright)=1-2(1)=1-2=-1 \\ h\mleft(5\mright)=1-2(5)=1-10=-9 \end{gathered}`

therefore, the range is

`\lbrace7,5,-1,-9\rbrace`

Step 2

graph the function

to plot the function just locate and mark each coordiante

`\begin{gathered} \left(-3,7\right) \\ \lparen-2,5) \\ \left(1,-1\right? \\ \lparen5,-9) \end{gathered}`

I hope this helps you

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