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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

A reflection across x-axis gives the negative (or opposite value) of itself, so g(x) = -f(x)

Assume f(x) = a x^4 + b x^3 + c x^2 + d x + e

Put those five values into the above equation to form five simultaneous equations. Solve them and use the a, b, c, d, e to calculate the value of 2007.