MATH SOLVE

4 months ago

Q:
# For each function, use the slope formula to calculate the rate of change between the points. In your final answer, include all of your calculations. F(x): (a,f(a)) and (b,f(b)) 1.) f(x)=1/2x−3 (0,f(0)) and (6,f(6)) 2.) f(x)=−x (−4,f(−4)) and (2,f(2)) 3.) f(x)=x2 (−2,f(−2)) and (0,f(0)) 4.) f(x)=x3 (−1,f(−1)) and (1,f(1)) 5.) f(x)=2x (0,f(0)) and (4,f(4))

Accepted Solution

A:

Answer:m = rate of change of the functions.1) m = 1/22) m = -13) m = -24) m = 15) m = 2Step-by-step explanation:Hi there!For the points (a, f(a)) and (b, f(b)), the rate of change between them, m, is calculated as follows:m = f(b) - f(a) / (b - a)Then:1) f(x) = 1/2 x - 3f(0) = 1/2 · 0 -3 = -3f(6) = 1/2 · 6 - 3 = 0m = f(6) - f(0) /( 6 - 0)m = 0 - (-3) / 6 = 1/22) f(x) = -xf(-4) = -(-4) = 4f(2) = -2m = f(2) - f(-4) /(2 - (-4)m = -2 - 4 / 2 + 4m = -6/6m = -13) f(x) = x²f(-2) = (-2)² = 4f(0) = 0² = 0m = f(0) - f(-2) / 0 - (-2)m = 0 - 4/ 2 = -24) f(x) = x³f(-1) = (-1)³ = -1f(1) = 1³ = 1m = f(1) - f(-1) / 1 - (-1)m = 1 - (-1)/ 2m = 2/2 = 15) f(x) = 2xf(0) = 2 · 0 = 0f(4) = 2 · 4 = 8m = f(4) - f(0) / (4 - 0)m = 8 - 0 / 4m = 2