b What is the zero of a function? Use one of the forms of writing the equation of a linear function.
A
aExample Solution: f(x)=2x-6
B
bExample Solution: g(x) = 3(x-4)
Practice makes perfect
a Recall that a zero of a function is a value of x such that f(x)= 0. In other words, it is the value of x for which the function intercepts the x-axis. Notice that there are infinitely many possible linear functions that satisfy this condition.
Since the only requirement for the function is that its graph must pass through the point ( 3, 0), the slope of the line can take any value we want. We can choose an arbitrary value for the slope and, since we know a point on the line, we can use the point-slope form to write the equation.
y- y _1 = m(x- x_1)
In this equation m is the slope of the line and ( x_1, y _1) is a known point. We can choose m= 2 and substitute it together with our point of intersection into the point-slope form.
In order to use function notation, we can replace y with f(x). As a result, we obtain the linear function f(x) = 2x-6. This function has a zero at x=3, as required.
b Now, to find a linear function with a zero at x=4, we will proceed just as we did in Part A. Let's choose a value for the slope, for example m= 3. We know that the line must pass through the point ( 4, 0). Therefore, let's substitute these values into the point-slope form.
