Which function represents a vertical stretch of an exponential function? х
*x)=3
o f(x)= 5 (3)
3
O
f(x) = (3) 2x
()
f(x)=3
NI

the correct answer is 45x

9×5=45 then add the x

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.