Answer:
f(x)= -|x + 1| + 1
Step-by-step explanation:
This is an absolute value equation, because it's that v-shape that let's us know it will be one. The standard form is
f(x)= a|x - h| + k, where h is the horizontal shift, k is the vertical shift, and a is the dilation factor.
We know that the graph is moved up one, because its vertex is at y = 1. So k = 1.
f(x)= a|x - h| + 1
We also know that it must be negative, because it's upside-down, so <em>put the negative outside the absolute value, not inside.</em>
f(x)= -|x - h| + 1
Lastly, the horizontal shift is left one, so we know that h = -1.
f(x)= -|x - -1| + 1
x minus a negative one equals x plus one, so
<u>f(x)= -|x + 1| + 1 </u>is our final answer.
Answer:
x = 180 - (37 + 53)
Step-by-step explanation:
-7/16 - 1/4 - 5/16
1. -7/16 - 4x1/4x4 - 5/16
2. -(7/16 + 4/16 + 5/16)
3. -7 + 4 + 5/16
that will add up to be 16/16 then cancel them out and you get for your answer -1
Answer:
20:5
Step-by-step explanation:
find how many parts (5)
25/5=5 (1 part)
5*4=20
5*1=5
I'll go over part A.
What's happening is that we are plugging some unknown number x into the function, and getting -1 as the result. The function rule is 3*x-7 which translates to "multiply the input number by 3, then subtract off 7"
Notice how multiplication comes first and then we subtract. This is following the order of operations PEMDAS (some books may call it BEDMAS depending on your region). The M for multiplication comes before the S for subtraction.
To isolate x, we follow the order of operations in reverse. We undo the "subtract off 7" then we undo the "multiply by 3"
So this is how it all works out
f(x) = 3x-7
-1 = 3x-7 .... replace f(x) with -1
3x-7 = -1
3x-7+7 = -1+7 ... add 7 to both sides to undo the "-7"
3x = 6
3x/3 = 6/3 ... divide both sides by 3 to undo the "multiplication"
x = 2
Therefore, if the input is 2, then output is -1
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Let's plug x = 2 into the function and see what happens
f(x) = 3x-7
f(2) = 3*2-7 .... replace x with 2
f(2) = 6-7 .... multiply
f(2) = -1 .... subtract
The input x = 2 leads to the output -1
So this confirms that x = 2 is the proper answer for part A
