please can i get help with question please asap

Question

Question 1:The number of cars sold per month can be modeled by f(x) = 0.03x³ + 0.4x² + 0.7x + 75, where x represents the number of months since April. Let g(x) = f(x) − 25. Which of the following gives the rule for g and the correct explanation of the meaning of the transformation in terms of monthly car sales?

A.) 0.03x3 + 0.4x2 + 0.7x + 50

vertical shift 25 units down

decrease of 25 units per month

B.) −0.03x3 + 0.4x2 − 0.7x + 100

vertical shift 25 units up

increase of 25 units per month

C.) 0.03x³ + 0.4x² + 0.7x + 100

vertical shift 25 units up

increase of 25 units per month

D.) 0.03x3 + 0.4x2 + 0.7x + 25

vertical shift 50 units down

decrease of 50 units per month

Question 2: The table shows the numbers of cars manufactured by a company for selected years. Identify a polynomial function for cars manufactured in thousands where x represents the years since 1990.

A.) P(x) = 0.2x³ + 0.5x² + 0.4x + 0.3

B.) P(x) = 0.5x³ + 0.5x² + 0.4x + 0.4

C.) P(x) = 0.2x³ + 0.2x² + 0.3x + 0.3

D.) P(x) = 0.5x³ + 0.2x² + 0.3x + 0.4

Question 3: Use finite differences to identify the degree of the polynomial that best describes the data.

A.) quartic

B.) cubic

C.) quadratic

D.) linear

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

Answer 1

Your picture links for question 2 and 3 are not showing up or working properly, so unfortunately I won't be of much help with those questions without being able to see the entire question. But I can help with the first problem!

For question 1, when you subtract 25 from an equation as defined by g(x) that means that f(x) will shift up or down that amount. Since it is minus 25 that will be a downward shift. If they had added 25 instead that would have meant it shifted up 25. Let's say instead they said g(x) =f(x+25) then that would have been a horizontal shift instead of a vertical one. Since it is a plus 25 in parenthesis that means it would shift left 25 (its always the opposite sign). If it had said f(x-25) then that would have been a shift right 25. So the thing to remember is that if a number is added or subtracted at the end not in parenthesis that is a vertical shift and the sign of that number indicates which direction up or down. If the number is added or subtracted from x in parentheses, that is a horizontal shift and you want to switch the sign to determine which direction the function moved left or right.