What is the graph of y = cos(x) +3?

Given function: f(x) = cos x + 3

To Draw: Graph of f(x)

As we know graph of trigonometric function cos x is a continuous graph with amplitude 1 .i.e., graph is 1 unit above and 1 unit down from the middle of graph.

If we add a constant to the trigonometric function it does not change any thing it just shift the function up or down according to value of constant.

Here 3 is added to cos x ⇒ Gr pah of cos x will be shifted 3 units upward.

Therefore, The graph we obtain is attached.

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.