How do you find the explicit function of a graph and a table?
f(x) = ______x + _______
I am extremely confused please help me.
since I have no table, it's kinda hard to say, eh?
Check the table you have, and if y increases by m each time x increases by 1, the slope is m.
So, y = mx+ b
to find b, see what y is when x=0. That will be b, since m*0+b = b
Does anybody have any idea on how to do this? Please I really need help!
Thanks Steve
To find the explicit function of a graph or a table, you need to observe the pattern and relationships between the given values. Let's go step by step:
1. Graph Method:
- Examine the given graph and identify two points on the graph (x1, y1) and (x2, y2).
- Calculate the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1).
- Determine the y-intercept (b) by selecting any point on the line (x, y) and substituting its values into the slope-intercept form equation: y = mx + b. Solve for b.
- Write down the equation in the form: f(x) = mx + b, where m is the slope and b is the y-intercept.
2. Table Method:
- Examine the given table and look for a consistent pattern between the x-values and y-values.
- Determine if there is a constant rate of change between the x-values and y-values. If so, this suggests that the equation is linear.
- Calculate the slope (m) using the formula: m = (change in y) / (change in x) for any two corresponding points.
- Identify the y-intercept (b) by looking at the y-value when x = 0 (assuming there is one in the table).
- Write down the equation in the form: f(x) = mx + b, where m is the slope and b is the y-intercept.
Example:
Let's say we have a graph with two points (2, 4) and (5, 7).
Using the graph method:
- Calculate the slope: m = (7 - 4) / (5 - 2) = 3 / 3 = 1.
- Determine the y-intercept: Selecting point (2, 4), substitute into y = mx + b equation: 4 = 1 * 2 + b. Solve for b: b = 2.
- The explicit function is: f(x) = 1x + 2.
Using the table method:
- Calculate the slope: m = (7 - 4) / (5 - 2) = 3 / 3 = 1.
- Determine the y-intercept: Looking at x = 0 (not in the given table), we can assume y = 2.
- The explicit function is: f(x) = 1x + 2.
In both methods, the resulting equation is f(x) = x + 2.