Beginner algebra help, I’m so lost thank u !!

Answers:

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Explanation:

The int function is the nearest integer function, and it's also called the floor function. It rounds things down to the nearest integer. The term 'down' is important.

So for example,

The reason why it's called the floor function is because we round down to the nearest floor.

In contrast, the ceiling function will have us always rounding up. Using the ceiling function on a number like 2.00007 will round up to 3 even though it's much closer to 2.

I recommend you practice a bit with this floor function to get a better grasp on it if you're still stuck. Feel free to ask any questions about it.

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With those examples out of the way, we can now determine the output of the function int(3x)

It's a similar idea, but we'll be multiplying each input x value by 3 first, then applying the int function.

If x = 1.9, then 3x = 3*1.9 = 5.7

Then note how int(3x) = int(5.7) = 5

Therefore, f(1.9) = 5

This is how the steps could look like

f(x) = int(3x)

f(1.9) = int(3*1.9)

f(1.9) = int(5.7)

f(1.9) = 5

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Repeat those steps but now using x = 2.9

f(x) = int(3x)

f(2.9) = int(3*2.9)

f(2.9) = int(8.7)

f(2.9) = 8

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And finally, we need to plug in x = -2.1

f(x) = int(3x)

f(-2.1) = int(3*(-2.1))

f(-2.1) = int(-6.3)

f(-2.1) = -7

Be careful not to round down to -6 as this is incorrect. Use the vertical number line if needed.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: