AndreArgo said:Y=f(x)
which passes through points:
(-1,3) and (0,2) and (1,0) and (2,1) and (3,5)
second function is defined: g(x)=2f(x-1)
Calculate g(0)
Calculate g(1)
Calculate g(2)
Calculate g(3)
Just figured it out. Thank you MarkMarkFL said:Hello, and welcome to MHB! (Wave)
We are given:
\(\displaystyle g(x)=2f(x-1)\)
We are also given 5 points in the form:
\(\displaystyle (x,f(x))\)
And so:
\(\displaystyle g(0)=2f(0-1)=2f(-1)=2\cdot3=6\)
Does that make sense? Can you continue?
To calculate g(x) for a given function f(x) passing through two points, you can use the slope formula: g(x) = (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. You can then substitute the values for x and y from the two points into the formula to find the value of g(x).
Yes, you can calculate g(x) for a function passing through more than two points. You will need to first find the slope between each pair of points, and then take the average of these slopes to get the overall slope. You can then use this slope value to calculate g(x) for any given value of x.
If the function f(x) is not a straight line passing through the points, you will not be able to use the slope formula to calculate g(x). Instead, you will need to use a curve fitting method, such as regression analysis, to find an equation that closely fits the given points. You can then use this equation to calculate g(x) for any value of x.
No, there is no specific order in which you need to input the points when calculating g(x). As long as you correctly match the x and y values for each point, the result will be the same. However, it is always a good practice to input the points in a consistent and organized manner.
Yes, you can use the same method to calculate g(x) for any type of function, as long as the function passes through the given points. However, for non-linear functions, you will need to use a curve fitting method to find the equation of the curve passing through the points before calculating g(x).