Question

Number 1 A to D and number 2 A to C....?

Answer 1

A polynomial function is something that is in the form ax^n+bx^(n-1)...+c. For (a), we see that 4x^3 is the highest power of x, so everything after it must be to the power of an integer less than 3 and more than -1. Since -3x^2 is to the power of 2, that works. Since 2 is 2x^0, that works too (since anything to the power of 0 is 1)

For (b), we get that .4x^3 is, again, to the highest power in this expression. However, sqrt(x) is x to the power of 1/2, which is not an integer and therefore making it not a polynomial function.

I challenge you to do c and d on your own using what I said!

For 2, we have f(3)=2 and f(4)=7. That means that we have the coordinates (3,2) and (4,7). Since the equation is y=mx+b, m(the slope) is found by 
(x1-x2)/(y1-y2), x is the first number is the point, so 3 and 4 are both x values. Y values are the second number. (3-4)/(2-7)=-1/-5=1/5, which is the slope, making our equation y=(1/5)x+b. Since y and x must always stay that way (in the final equation) we just need to find b. To find it, we can plug in 3 and 2 for x and y respectively, getting 2=(1/5)*3+b=0.6+b. Subtracting 0.6 from both sides, we get b=1.4, making the equation y=(1/5)*x+1.4.

I challenge you to do B and C on your own using what I said!