Question

For the following linear functions, create an input-output table, and graph the line.

1) f(x) = -2 + 2x
2) f(x) = x + 5

Answer 1

To graph the linear functions, create an input-output table by selecting several x-values and computing the corresponding y-values. Then, plot these points on a graph, label the axes, and draw a straight line through the points to represent each function's graphical dependence of y on x.

Step-by-step explanation:

To create an input-output table and graph the lines for the linear functions f(x) = -2 + 2x and f(x) = x + 5, we will select a range of x-values and calculate the corresponding y-values (outputs) for each function. Here's a step-by-step process:

• Choose a range of x-values, for example, -2, -1, 0, 1, 2.
• Calculate the y-values using the given functions:
• For f(x) = -2 + 2x, the table will look like this:

xf(x)-2-6-1-40 -21022

• For f(x) = x + 5, the table will look like this:

xf(x)-23-140 51627

Plot these points on a Cartesian plane, ensuring you label the graph with f(x) and x. Then, draw a straight line through the points of each function. This line is the graphical representation of the function, displaying the dependence of y on x.