The function represented by the given table is f(x) = -2x+1. This is obtained by graphing the table and using the standard form of a linear graph.
What is the standard form of a linear graph?
The standard form of a linear is f(x) = mx+c. Where m is the slope of the line and c is the y-intercept. This is also said to be the slope-intercept form of a line.
How to find the function represented by the table?
- We know that the table represents a graph y=f(x)
- Consider any two points as (x,y) coordinates and solve the slope m with the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
- Apply any of the points from the table to the equation y=mx+c for finding the c value
- Thus, the obtained equation will represent the function of the table.
Calculating the function for the given table:
Plotting the graph for the given values from the table as (-1,3), (0,1), (1,-1) and (2,-3).
Thus, the graph is linear, the standard form is y=mx+c.
Finding the slope for the points (-1,3) and (0,1):
[tex]m=\frac{1-3}{0+1}=-2[/tex]
Thus, on substituting in the standard form
y = -2x+c
From the point (-1,3), x=-1 and y=3
So,
3 = -2(-1)+c
⇒ c = 3 - 2
⇒ c = 1
Thus, the function of the given table is written as y = -2x+1 or f(x) =-2x +1.
Therefore, option A is correct.
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