Question

The function h is defined as follows for the domain given.

h(x)=2x+1, domain = {-4, -2, 1, 3}
Write the range of h using set notation. Then graph h.

Answer 1

Range = {-7, -3, 3, 7}

See the attachment for the graph of the function.

Explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Given function: h(x) = 2x + 1

Given domain: {-4, -2, 1, 3}

To find the range of the function, input the values of the domain into the function to calculate the corresponding y-values.

`\begin{aligned}x=-4 \implies h(-4)&=2(-4)+1\\&=-8+1\\&=-7\end{aligned}`

`\begin{aligned}x=-2 \implies h(-2)&=2(-2)+1\\&=-4+1\\&=-3\end{aligned}`

`\begin{aligned}x=1 \implies h(1)&=2(1)+1\\&=2+1\\&=3\end{aligned}`

`\begin{aligned}x=3 \implies h(3)&=2(3)+1\\&=6+1\\&=7\end{aligned}`

Therefore, the range of the given function is {-7, -3, 3, 7}.

To graph the function:

• Plot the ordered pairs: (-4, -7), (-2, -3), (1, 3), (3, 7).
• Draw a straight line through the plotted points.

(See attachment).