The function f(x) passes through the points (−4, 6) and (−2, 3)
The function g(x) is represented by the equation g(x)=1/2x^2−3
Which of the following statements is true of these two functions?
The function f(x) passes through the points (-4, 6) and (-2, 3). This means that when x is -4, f(x) is 6 and when x is -2, f(x) is 3. We can use these points to find the equation of f(x).
Using the equation of a straight line in point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using the point (-4, 6):
y - 6 = m(x - (-4))
y - 6 = m(x + 4)
Using the point (-2, 3):
3 - 6 = m(-2 + 4)
-3 = 2m
m = -3/2
Therefore, the equation of f(x) is:
y - 6 = (-3/2)(x + 4)
Simplifying:
y - 6 = (-3/2)x - 6
y = (-3/2)x
On the other hand, the equation of g(x) is:
g(x) = (1/2)x^2 - 3
From these equations, we can see that f(x) is a linear function (the highest power of x is 1) while g(x) is a quadratic function (the highest power of x is 2). Therefore, the statement "f(x) is a linear function and g(x) is a quadratic function" is true.