please help!!1

Question

Write an example of a polynomial function for each as described below.

a) A cubic function with a positive leading coefficient and a constant term of -2.

b) A quadratic function with a negative leading coefficient and a constant term of 3.

c) A linear function with a positive slope and a y- intercept of 5.

d) A polynomial function with a degree of 3, a negative leading coeficient,and a total of 4 terms.

e) A polynomial function that starts in quadrant 3 and ends in quadrant 1 and is NOT  a linear function.

Answer 1

(a)

A Cubic function is whose degree of Equation is 3 and the constant term is -2

Let us consider at cubic equation.

It is in the form of ax³+bx²+cx+d = 0.

Now the Equation has positive leading coefficient which means a is positive value.

Let us consider a = 4. b = 2, c = 3 and constant d = -2.

Therefore the Equation is 4x³+2x²+3x-2 = 0.

Therefore an example for Cubic function with positive leading coefficient and the constant term is -2 is 4x³+2x²+3x-2 = 0.

Answer 2

(b)

A quadratic function with negative leading function and constant term is 3.

Let us consider a Quadratic function.

It is in the form of ax²+bx+c = 0.

Quadratic Equation has negative leading coefficient which means a < 0.

Constant trem is c = 3.

Let us consider a = -2 and b = 3

then the Quadratic Equation is -2x²+3x+3 = 0.

Therefore the example for quadratic function with negative leading function and constant term is 3 is -2x²+3x+3 = 0.

Answer 3

(c)

A linear function with a positive slope and a y- intercept of 5.

Let us consider a linear Equation.

It is in the form of y = mx + b.

Given that slope is a positve number, so let m = 2

Given that y intercept is 5.

Y intercept is a graph or a point intersect with y-axis where the value of x = 0

then y= b

The Y - intercept is 5 then b = 5

Therefore the linear Equation is y = 2x+5

Therefore A linear function with a positive slope and a y- intercept of 5 is y = 2x + 5.

Answer 4

(d)

A polynomial function with a degree of 3, a negative leading coeficient,and a total of 4 terms

The Polynomial function with degree 3 is ax³+bx²+cx+d = 0.

The leading coefficient value is negative which means a < 0.

Let us us consider a = -2

There are total four terns in the equation.

Let us consider b= 1, c = 3 and d = 5

Then the polynomial function is -2x³+x²+3x+5 = 0.

Therefore the example for polynomial function with a degree of 3, a negative leading coeficient,and a total of 4 terms is -2x³+x²+3x+5 = 0.

Answer 5

(e)

A polynomial function that starts in quadrant 3 and ends in quadrant 1 and is NOT  a linear function.

A even degree function starts in IIrd Quadrant and ends in Ist Qudrant.

A odd degree function starts in IIIrd Quadrant and ends in Ist Qudrant.

Therefore degree of the Equation can be 1, 3, 5 and so on.

Given that ploynomial function is not a linear function then Degree can be 3, 5 and so on.

Let us consider that degree of the function is 5

Then the Equation is in the form of ax⁵+bx⁴+cx³+dx²+ex+f = 0.

Let us consider a = 1, b = 2, c = 3, d =4, e = 5 and f = 1

Therefore the function is x⁵+2x⁴+3x³+4x²+5x+1 = 0.

Therefore A polynomial function that starts in quadrant 3 and ends in quadrant 1 and is NOT  a linear function is x⁵+2x⁴+3x³+4x²+5x+1 = 0.