Graph each function.

1. y = x^2 + 5

Which numbers should I choose as the x-values?

Don't pick numbers which yield a large y value, and thus hard to plot

I would pick
x = ±1, ±2, ±3

that gives you 6 points, and a good indicator of the graph.

X

-2
-1
0
1
2
3
4

Include x = 0 for sure :)

To graph the function y = x^2 + 5, you need to choose a range of x-values. The choice of x-values will determine the shape and spread of the graph.

To get started, you can choose a set of x-values within a certain range that you think would be representative. For example, you can start by choosing some integer values for x, such as -3, -2, -1, 0, 1, 2, and 3. This will give you a good sense of what the graph looks like around these key points.

However, to obtain a more accurate and detailed graph, it is advisable to choose a wider range of x-values. You can choose both positive and negative values, and include decimals or fractions. Additionally, you can include values that are close to any critical points such as the vertex or points of intersection with the x-axis.

For instance, you may choose a range of x-values from -5 to 5, including both the negative and positive numbers. You can then increment the x-values by 1 or 0.5, depending on how detailed you want your graph to be.

By choosing a suitable range of x-values and plotting corresponding y-values obtained by substituting those x-values into the function, you can accurately graph the function y = x^2 + 5.