Question

Graphs of Polynomial Functions Gizmo

5 Answer Review


1. What are the degree and leading coefficient of the function y=4x2-3x+7?


A. degree=4 leading coefficient=2

B. degree=2 leading coefficient=4

C. degree=2 leading coefficient=7

D. degree=3 leading coefficient=4


2. What is the lowest degree of the function graphed here? (image is attached to this)


A. 1

B. 2

C. 3

D. 4


3. what is the maximum of x-intercepts that can be found on a graph with equation y=ax5+cx2+f? (the values a, c, and f are real numbers)


A. 2

B. 3

C. 4

D. 5


4. Which polynomial function has a y-intercept of 3?


A. y=2x4+x2-3

B. y=3x2+4

C. y=-4x7-5x+3

D. y=9x3+3x2


5. What is the end behavior of y=-2x13+25x8-3 as x approaches infinity?


a. y=-3

b. y=13

c. y approaches infinity

d. y approaches negative infinity

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