hello can someone help with question i have been stuck for hours

Question

Question 1:Let f(x) = x³ + 5x² − 7x −8. Identify the function g that reflects f across the x-axis.

A.) g(x) = −x³ − 5x² + 7x + 8

B.) g(x) = x³ + 5x² + 7x + 8

C.) g(x) = x³ + 5x² + 7x − 8

D.) g(x) = −x³ − 5x² − 7x − 8

Question 2: The table shows the numbers of cars manufactured in thousands by a company for selected years. Use a calculator to write a quartic model for the number of cars manufactured in a given year since 2000. Then use the model to estimate the number of cars manufactured in 2007.

A.) (x) ≈ 0.572x⁴ − 15.63x³ + 146.273x² − 523.325x + 687.334

The estimated number of cars manufactured in 2007 is about 203.

B.) f(x) ≈ 0.423x³ − 12.463x² + 123.485x − 223.309

The estimated number of cars manufactured in 2007 is about 178.

C.) f(x) ≈ 0.572x⁴ + 15.63x³ − 146.273x² − 523.325x + 687.334

The estimated number of cars manufactured in 2007 is about 203.

D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309

The estimated number of cars manufactured in 2007 is about 178.

Please give and only give explanation and solution.

Answer 1

QUESTION 1:

A function f(x) reflected over the x-axis is: -f(x). So,

f(x) = x³ + 5x² - 7x - 8

reflected over the x-axis is:

-f(x) = -x³ - 5x² +7x + 8

Correct answer is A.

g(x) = -x³ - 5x² +7x + 8