Sara A.
asked • 11/30/23How do I find the f(x) in a graph
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2 Answers By Expert Tutors
You can find f(x) simply by substituting in the given value of x into the equation for f(x) and evaluating that expression.
For instance if f(x) = 3x + 6 and you want to know the f(x) value corresponding to x=4, then 3*(4) +6 = 12 + 6 = 18 = f(4).
If you have a graph of f(x), all you have to do is locate the x point (4 for example) and construct a vertical line through x=4. Where the vertical line intersects the function's graph is f(x) and has the coordinate point (x,f(x)).
Ellsworth J. answered • 11/30/23
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I'm going to assume you mean that you have the graph of a line in the coordinate plane (with the grid, the x and y axis, and all that good stuff), and you need to determine f(x) from that graph... right?
Sara A.
yes that
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12/01/23
Ellsworth J.
Well... the short answer is that your line will have an equation of the form y = mx + b, where m is the line's slope, and b is the y-intercept (where it crosses the y-axis). You can get both of these from looking at the graph. b is the value of y where the line crosses the y-axis. So if the line crosses the y-axis at y = 1, then b = 1. If it crosses at y = -3, then b = -3. m is the line's slope. Pick any two points on the line, and between them, MOVING LEFT TO RIGHT, figure out the "rise" (how far up or down you move; up is positive, down is negative) and the "run" (always positive, since you are moving left to right). m = slope = rise / run Once you have m and b, you're done. Plug them in. For example, if you calculate that the slope (m) of your line is 2, and the y-intercept is at y = 5 (which means b = 5, too), then y = mx + b y = 2x + 5 or, in this context, y is f(x), so f(x) = 2x + 5 is the equation of the line. If the y-intercept were at y = -3, then b = -3 and y = 2x + (-3) or y = 2x - 3 f(x) = 2x - 3
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12/01/23
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James L.
Usually equations come in the form of f(x)=2x+5 for example (f(x) is the same as y on a graph). Other equations look like this f(x)=2(x^2)+5. And others f(x)=e^4+50395. Some graphs are easy to find the equation to. And others (f(x)=e^4+50395) are usually not worth hurting your head over. If you have a visual graph and you want to find the equation for that graph, you need to match it up with other graphs that you know. Does my graph look like f(x)=x, or f(x)=x^2, or f(x)=x^3, etc. Once you know the basic shape that the graph follows, you need to look up the methods for identifying the equations values. As an easy example, if your equation is a straight line, but angled up like this / then you would follow the form (y -y1) =[(y2 - y1) / (x2 - x1)] (x - x1) You would pick two points on the graph (x1,y1) and (x2,y2). Then you insert the values into the above equation and do your well known math skills to add and subtract the numbers (algebra) to get an equation of the form y=mx+b which equals f(x)=mx+b. Each graph shape will have a different method, so you have to look up the methods for the specific kind of graph that you have. Or, if it isn't homework but the real world, then you would make a computer analyze the graph and pick the best fit.11/30/23