Question

Graph the function and make a X and Y table.

Answer 1

See the attached graph.

Explanation:

To graph the function y = 4√x - 4 and create an x and y table of points, choose a range of x-values, calculate the corresponding y-values, and then plot the points on a graph.

Since the value under the square root sign cannot be negative, the domain of the function is restricted to x ≥ 0. Therefore, a suitable range of x-values for the given coordinate plane is 0 ≤ x ≤ 8 (since the greatest x-value on the coordinate plane is x = 8).

Calculate the corresponding y-values (rounded to one decimal place) by substituting the x-values into the given function, and enter the (x, y) points into a table:

`\begin{array}c\cline{1-2}x&y\\\cline{1-2}0&-4\\\cline{1-2}1&0\\\cline{1-2}2&1.7\\\cline{1-2}3&2.9\\\cline{1-2}4&4\\\cline{1-2}5&4.9\\\cline{1-2}6&5.8\\\cline{1-2}7&6.6\\\cline{1-2}8&7.3\\\cline{1-2}\end{array}`

Plot the points from the table on the given coordinate plane, then draw a smooth curve from (0, -4) through the plotted points. Add an arrow to the end of the curve at (8, 7.3) to indicate that the curve continues in that direction.

Answer 2

See below

Explanation:

`\sf y = 4√(x) - 4`

To graph the function
`\sf y = 4√(x) - 4` and create an x and y table, we can select a range of x-values, calculate the corresponding y-values, and then plot the points on a graph.

we can find the value of y after substituting any value of and solve for y.

Here's a table with some example values and the graph:

`\boxed{\begin{aligned} x &| y \\\\ 0 &| -4 \\\\ 1 &| 0 \\\\ 4 &| 4 \\\\ 9 &| 8 \\\\ 16 &| 12 \end{aligned}}`

For Graph: See Attachment

The graph represents the function and passes through the points (0, -4), (1, 0), (4, 4), (9, 8), and (16, 12).

It's a curve that starts at (-4, 0) and increases as x increases.