Question

HELP PLEASE ASAP

The change in the water level of a water tower is modeled by a polynomial function, W(x) = -5x3 + 7x - 2. Which components of the equation relay information on the end behavior of the graph and describe the end behavior of the graph. Describe how many x-intercepts of W(x) can be found and which components of the equation relays that information. Using graphing technology find the approximate x-intercepts so that the city Water Department can predict when there will be no change in the water level

Answer 1

Answer: a) degree and sign

b) end behavior: left side → +∞, right side → -∞

c) x-intercepts: x = -1.3, 0.3, 1.0

Explanation:

end behavior can be determined by two things:

1) the degree of the polynomial:

• if the degree is an even number, then the end behavior will be the same for both the left and right sides.
• if the degree is an odd number, then the end behavior will be different for both the left and right sides.

2) the sign of the leading coefficient:

• If the leading coefficient is positive, then the end behavior of the right side goes to positive infinity
• If the leading coefficient is negative, then the end behavior of the right side goes to negative infinity

W(x) = -5x³ + 7x - 2

Degree: 3 (odd)

Leading Coefficient: negative

So, end behavior is: right side goes to negative infinity, right side goes to positive infinity.

See attachment for x-intercepts. I set the x-axis to represent tenths