Answer:
As the distance between the y-intercepts of f(x) and g(x) is 3.
So, the y-intercept of f(x) is 3 units below g(x), as shown in attached figure a.
Step-by-step explanation:
Let us consider the equation of straight line in the form of slope-intercept form such as:
[tex]y = mx + b[/tex]
where m is the slope of the line and b is the y-intercept.
Determining the y-intercept of f(x) = x - 1
As the given function f(x) = x-1 is in the form of [tex]y = mx + b[/tex].
So, the y-intercept will be -1.
y-intercept can also be computed by putting x = 0, as at y-intercept the value of x is zero.
f(x) = x - 1
y = 0 - 1 ⇒ y = -1
Determining the y-intercept of g(x) = x + 2
As the given function g(x) = x + 2 is in the form of [tex]y = mx + b[/tex].
So, the y-intercept will be 2.
y-intercept can also be computed by putting x = 0, as at y-intercept the value of x is zero.
g(x) = x + 2
y = 0 + 2 ⇒ y = 2
Determining the distance between the y - intercepts of f(x) and g(x)
- The y-intercept of f(x) = x - 1 is -1.
- The y-intercept of g(x) = x+2 is 2.
So, the distance between the y - intercepts of f(x) and g(x): 2 - (-1) = 3
So, the y-intercept of f(x) is 3 units below g(x), as shown in attached figure a.
Keywords: y-intercept, graph, function
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