Use the graphs of f(x) = 2
x
and g(x) = 1
-3-x
to determine the solutions to f(x) = g(x).

A

Step-by-step explanation:

The solution to f(x) = g(x) occurs where the two graphs cross.  That's at the point (-2, -1).

Answer A.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.