When you reflect a function in the <em>x</em>-axis, the first coordinate of a point stays the same, and the second coordinate changes sign (what was positive is now negative and vice versa). See the attached picture.
Question 11: f(x) = -5x + 2. The function changes to its opposite, so g(x) = -(-5x + 2) = 5x - 2.
When you reflect a function in the <em>y</em>-axis, the first coordinate of a point changes to its opposite, but the second coordinate stays the same. Replace <em>x</em> with -<em>x</em> .
Question 14: f(x) = |2x - 1| + 3. Replacing <em>x</em> with -<em>x</em> produces g(x) = |2(-x) - 1| + 3 which simplifies to g(x) = |-2x -1| + 3.
Question 15 works the same way as #14.
Answer:
(2x - 3) • (x + 4)
Step-by-step explanation:
Step 1 :
Equation at step 1 :
(2x2 + 5x) - 12
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+5x-12
The first term is, 2x2 its coefficient is 2 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 2 • -12 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is 5 .
-24 + 1 = -23
-12 + 2 = -10
-8 + 3 = -5
-6 + 4 = -2
-4 + 6 = 2
-3 + 8 = 5
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 8
2x2 - 3x + 8x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-3)
Add up the last 2 terms, pulling out common factors :
4 • (2x-3)
Step-5 : Add up the four terms of step 4 :
(x+4) • (2x-3)
Which is the desired factorization
Let's use 50 cents as the price of the item
Two for the price of one = $.50 for two (or $.25 each)
Three for the price of two = $1.00 for 3 or approximately $.33 each
Buy one get 25% off the 2nd means $.50 + (.125 which is 25% of $.50) for a total of $.625 or about $.63 ($.315 or about $.32 each)
Buy Two get 50% off the 2nd means $.50 for the first and $.25 for the 2nd for a total of $.75 or $.375 - about $.38 each
We can see that two for the price of one is the best value since you save $.25 off of $.50 (that's half) and that buy two get 50% off the 2nd is the smallest price reduction since the $.50 item only goes down to $.38 or twelve cents off.
This would work no matter what the cost of the item. The savings would still be in the same proportions.
Answer:
Step-by-step explanation:
y=mx+b
m=(y2-y1)/(x2-x1)
m=(90-65)(/(200-100)=25/100=1/4
y=x/4+b, using point (100,65)
65=100/4+b
65=25+b
b=40
y=x/4+40 or more neatly
y=(x+160)/4
Following these steps you should have no problem with second problem.
