How many turns will the graph of f(x) = 3x5 -2x4 + 7x2 -9x + 8 have?

The number of turns of graph for are 4

Step-by-step explanation:

We need to find the number of turns the graph of have?

Turns of graph:

The graphs turns when it changes from increasing to decreasing (rise to fall) or decreasing from increasing (fall to rise)

Turns of graph for a polynomial

A polynomial having degree n will have maximum n-1 turns.

So, for the given polynomial

We need to find degree

The highest exponent of the polynomial is the degree of polynomial

So, Degree n = 5

Number of turns = n - 1 = 5-1 =4

So, the number of turns of graph for are 4

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: