Question

The function 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

Given: The function below

`\begin{gathered} h(x)=1-2x \\ Domain:\lbrace-3,-2,1,5\rbrace \end{gathered}`

To Determine: The range and the graph of h9x)

Solution

Please note the ddomain is the input of the function. Let us use the values of x (domain) to get the range as shown below

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

Hence, the range is {7, 5, -1, -9}

Let use the domain, the set of x-values to plot a graph against the corresponding y- values

The table of values showing x-values and corresponding y-values is

The graph of the domain and the range values is as shown below