Suppose y=f(x) + k. what effect does k have on the parent function

Adding 'k' to translates it 'k' units upwards.

Step-by-step explanation:

We are given that,

The parent function, is changed to

That is, transformation is applied to in order to obtain .

As, we can see that the constant 'k' is added to the parent function.

This means that, the function is shifted 'k' units upwqards.

Hence, adding 'k' to translates it 'k' units upwards.

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.