How to describe the transformation from the parent graph

The parent function get shifted up 4 units.

Step-by-step explanation:

Remember, if f(x) ⇒ f(x) + h, then f(x) gets shifted up h units.

Also, if f(x) ⇒ f(x - h), then f(x) gets shifted right h units.

Right now, it is f(x) ⇒ f(x) + h, so the graph gets shifted up h units.

h = 4

The parent function get shifted up 4 units.

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.