Final answer:
To find the equation for the function g(x) from two points, we assume a linear function and calculate the slope (m), followed by using one point to solve for the y-intercept (b). The resulting function equation is y = 0.7x + 1.5.
Step-by-step explanation:
To determine the equation for the function g(x), we need more information such as the type of the function (linear, quadratic, etc.) or additional points. However, based on the given points, (-5, -2) and (6, 5.7), if we assume that g(x) is linear, we can find a straight line equation in the form of y = mx + b where m is the slope and b is the y-intercept.
First, we calculate the slope using the formula m = (y2 - y1) / (x2 - x1). So, substituting the given values, we get m = (5.7 - (-2)) / (6 - (-5)) = 7.7 / 11 = 0.7.
Now, to find the y-intercept, b, we can substitute one point into the linear equation using the slope we just found. For example, using the point (6, 5.7), the equation is 5.7 = 0.7*6 + b, which simplifies to b = 5.7 - (0.7*6) = 1.5.
The equation of the function g(x) is therefore y = 0.7x + 1.5.