Question

3) y = 3x+1 A) Domain: x 2-1 Range: y so B) Domain: x 2-1 Range: y20 C) Domain: x 21 Range: y = 0 D) Domain: { All real numbers. Range: {All real numbers.

Answer 1

Given:

`y=\sqrt[]{x+1}`

Let's determine the domain and the range of the function.

The domain is the set of all possible values of x. It is also called the input.

The range is the set of possible values of y. It is also called the output.

• To find the domain, set the values in the radicand greater than or equal to zero and solve for x:

x + 1 ≥ 0

Subtract both sides by 1:

x + 1 - 1 ≥ 0 - 1

x ≥ -1

Therefore, the domain is all possible values greater or equal to -1:

x ≥ -1

To find the range, input the lowest value of the domain which is -1 and evaluate for y:

`\begin{gathered} y\ge\sqrt[]{-1+1} \\ \\ y\ge\sqrt[]{0} \\ \\ y\ge0 \end{gathered}`

Therefore, the range of the function is all integers positive interges including zero.

The graph is attached below:

ANSWER:

C) Domain: x ≥ -1

Range: y ≥ 0