x f(x) g(x)
2 5 0
3 7 1
4 9 2
5 11 3
What is the equation of g(x) ?
What is g(g(4)) ?
Name a point on the graph of g(x)
The table didn't turn out very good so here it is another way:
x: 2, 3, 4, 5
f(x): 5, 7, 9, 11
g(x): 0, 1, 2, 3
g(x) = x-2
g(4) = 2
g(g(4)) = 0
They have already provided you with four points on the g(x) curve. Ignore the data on f(x).
Notice f(x) and g(x) increase by two, and one, for each increase in x.
f(x)=2x+1
g(x)=x-2
Will that do it?
To find the equation of g(x) from the given table, we can observe the relationship between x and g(x). Looking at the table, we can see that as x increases by 1, g(x) increases by 1 as well. This indicates a linear relationship between x and g(x).
We can find the equation of g(x) using the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, since g(x) increases by 1 for every x increase of 1, the slope (m) is 1.
To find the y-intercept (b), we can look at the table and see that when x = 2, g(x) = 0. Therefore, when x = 2, we have the point (2, 0) on the graph of g(x).
Using the point-slope form, we can substitute one of the given points into the slope-intercept equation to find b:
0 = 1(2) + b
0 = 2 + b
b = -2
Now that we have the slope (m = 1) and the y-intercept (b = -2), we can write the equation of g(x):
g(x) = x - 2
To find g(g(4)), we need to substitute 4 into the equation of g(x):
g(g(4)) = g(4 - 2)
g(g(4)) = g(2)
g(g(4)) = 2 - 2
g(g(4)) = 0
Therefore, g(g(4)) = 0.
To name a point on the graph of g(x), we can choose one of the given points from the table. Let's choose the point (3, 1). Therefore, (3, 1) is a point on the graph of g(x).