Since the given relationship forms a straight line when plotted on a graph, we can conclude that the function $f$ is linear.
Let's find the slope of the line:
The change in $f(x)$ from 1 to 0 is 1 - (-1) = 2.
The change in $x$ from 1 to 0 is 1 - 0 = 1.
So, the slope is equal to change in $f(x)$ divided by the change in $x$: slope = (2)/(1) = 2.
To find the equation of the linear function, we need to find the y-intercept (or the value of $f(0)$). According to the mapping diagram, $f(0) = 1$.
Now that we have the slope (2) and the y-intercept (1), we can write the equation of the linear function as:
$f(x) = 2x + 1$.
Write a linear function $f$ with the given values.
A mapping diagram shows the relationship between x and f of x. An arrow is drawn from the x-value 1 to the f of x value negative 1. An arrow is drawn from the x-value 0 to the f of x value 1. An arrow is drawn from the x-value negative 1 to the f of x value 3.
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