Definition of a function:
Every x maps to a unique y
Notice Jan has 31 days and that’s it
March has 31 days and April has 30 days
But the number of days in February depends on leap year vs non leap year
So which month maps to two outputs?
(https://www.timeanddate.com/calendar/months/
Using substitution, we can rewrite the second equation as
3(-2x + 2x + 8) = 12
3(8) = 12
24 = 12
huh? NO solution
If we were to solve the second equation for Y=, we would get:
by distributing the 3
-6x + 3y = 12
add 6x to each side
3y = 6x + 12
Divide both sides by 3
y = 2x + 4 this is parallel to the first line y = 2x + 8 and therefore the lines will never meet
making the answer “No solution”
First look at the graph — looks super nonlinear and pretty exponential
Use the point (0,4).
We can eliminate answers (2) and (3), as if we substitute h=0, the output would be 6/5 and 4.2 as opposed to the 4 for the y value we are looking for.
Now we can use the point (1,8) to see if y = 8 when x = 1
For answer (4), if we substitute in x = 1, we get 2/3(1)^3 – 1^2 + 3(1) + 4 = 2/3 – 1 + 3 + 4≠ 8
Try answer (1): using order of operations: 4(2)^1 = 4(2) = 8
4(2)^2 = 16 and 4(2)^3 = 32. That’s it –2 points
You can also use Y= and check the table for a match:
This problem can be figured out using the idea of DOTS: Difference of Two Squares has a + and a -, such as x^2 – 9 = (x + 3) (x – 3). Therefore only answers 3 or 4 are possible! Answers (1) and (2) will result in a trinomial with 3 terms but we only want 2 terms.
Looking at answer (4), (8x^2)(8x^2) = 64x^4 and we are looking for 16x^4.
When x = 3, what is the y value for -2(3)^2 + 32? See the table above.
That’s it — 2 points!
