Question

Graphs of Polynomial Functions Gizmo

Answer 1

Answer:

 degree=2 leading coefficient=4

lowest degree = 3

maximum of 5 x-intercepts

$y=-4x^7-5x+3$ has y intecept 3

y approaches negative infinity

Step-by-step explanation:

(1) $y=4x^2-3x+7$

Highest exponent is the degree of the function

Highest exponent =2  so degree =2

Coefficient of x^2 is 4, so leading coefficient is 4

(2) from the graph we can see that

As x approaches infinity, the graph goes down

As x approaches -infinity, the graph goes up

The value of y goes on the opposite direction. So it is a odd degree function. If degree =1  then the graph should be a line

Here the graph is like a curve. Also we have 2 x  intercepts . Hence lowest possible degree of the function is 3

(3) y=ax^5+cx^2+f

Here , the degree of the equation is 5

So we will get maximum of 5 x-intercepts

(4) To find the function that has y intercept of 3, we plug in 0 for x in each function

$y=-4x^7-5x+3$

$y=-4(0)^7-5(0)+3= 3$

$y=-4x^7-5x+3$ has y intecept 3

(5) $y=-2x^{13}+25x^8-3$

Here degree is 13 that is odd  and leading coefficient is -2 ( negative)

Degree is odd and leading coefficient is negative so the graph of y goes down on the right side.

the graph of y approaches negative infinity when x approaches infinity