(! will give brainlest! ) what is the product of 1/2x - 1/4 and 5x^2 - 2x + 6 ? write your answer in standard form. can someone me with this? i understand how to multiply polynomials and such but this ones hard for me? explain.

The product of 1/2x - 1/4 and 5x^2 - 2x + 6 is 5/2x^3 – 9/4x^2 + 7/2x – 3/2

(a)(1/2x - 1/4) (5x^2 – 2x + 6)  

5/2x^3 – 5/4x^2 – 4/4x^2 + 2/4x +6/2x-6/4  

(I used 4/4 because it benefits me more when I visually see it)  

5/2x^3 -9/4x^2 + 14/4x – 6/4  

5/2x^3 – 9/4x^2 + 7/2x – 3/2

(b)No, because with the first part of the problem, the negative goes to ½ instead of 1/4x. When you find the product, instead of finding the exact same answer, you get 5/4x^3 – 3x^2 + 5/2x -3. The numbers when switched, change what they do. 1/4x just multiplies without a negative and ½ does with a negative.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.