Question

GRAPHING FUNCTIONS Graph the function. $$f(x)=-x+1$$

Short answer

The graph of the function \(f(x) = -x + 1\) is a straight line that intercepts the y-axis at the point (0,1) and has a negative slope of -1, so it decreases from left to right.

Step-by-step solution

Identify the Slope and Y-Intercept

The highest degree of the polynomial term for the function \(f(x)\) is 1, indicating that this is a linear function. A linear function is of the form \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept. Comparing \(f(x)=-x+1\) with this form, one can see that the slope \(m\) is -1 and the y-intercept \(c\) is 1.

Draw the Y-Intercept

The y-intercept is the point where the line crosses the y-axis. Here, the y-intercept is 1, so the first point will be at (0,1) on the y-axis. Make a dot at this point on the graph.

Apply the Slope

The slope, \(m=-1\), tells us that each step to the right on the x-axis will go one step down on the y-axis. This is due to the negative slope. Starting from the y-intercept, move one step to the right and one step down, this will be the second point at (1,0). Draw a line through these two points extending over the entire graph.