Answer:
g(x) = 2x +1
Explanation:
You want the complete table and the linear function that describes it, given the points (x, g(x)) = (-3, -5) and (-1, -1).
Differences
We note the differences between the x-values shown are -1 -(-3) = 2. The corresponding differences between those y-values is -1 -(-5) = 4.
This lets us fill in the values for x=1 and x=3 as being -1+4 = 3, and 3+4 = 7
We observe that the missing x-value corresponds to g(x)=1, which is halfway between g(x)=-1 and g(x)=3. That means its corresponding x-value will be halfway between x=-1 and x=1, at x=0.
The table is shown in the attachment.
Slope-intercept equation
The change in g(x) being 4 when the change in x is 2 means the slope is 4/2 = 2. The y-value of 1 when x=0 means the y-intercept is 1.
These are used to write the slope-intercept form of the equation:
y = mx +b . . . . . . slope is m, y-intercept is b
For a slope of 2 and a y-intercept of 1, the equation is ...
y = 2x +1
When we write that in "functional form", the expression g(x) replaces y:
g(x) = 2x +1