please someone please actually help me please asap

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.

Question 3: For f(x) = 3x² + 2x − 1, identify the rule for g(x) = f(x + 1) − 6 and its graph.

A.)

g(x) = (3x + 1)² + 2x + 1

B.)

g(x) = 3(x + 1)² + 2x + 1

C.)

g(x) = 3(x + 1)² + 2(x + 1) − 7

D.)

g(x) = 3(x + 1)² + 2(x + 1) − 7

Please just give and only give the explanation and the solution.

Answer 1

reflection about the x axis changes y to -y

if (x,y) is a point on the graph of the original function, then (x-y) is a point on the reflection about the x axis

so just change the sign of each term

f(x)= x^3 +5x^2 -7x - 8

g(x) =-x^3 -5x^2 + 7x + 8