Can someone help me solve this?!
2 answers:
To solve an inequality, you solve it just like an equation with an = sign
y-3 ≥ -12
Add 3 to both sides
y ≥ -9
What this means is that y could be any number as long as it’s greater than (bigger) or equal to -9, so y could equal -9, -3, 100, or 0 but could not equal -10,-11, -9.3, or anything less than -9
To graph this, first write in numbers below each of the lines. You want to show -9, a few numbers less than -9 and a few numbers greater than -9. It could look like this:
-11 -10 -9 -8 -7 -6 -5
Then, draw a filled in circle above -9. This shows that y can equal -9. Starting from where you drew the circle, draw an arrow to the right until the graph ends. This shows that y could be any of these numbers greater than -9, too.
I attached an example of a filled in number line for a different problem so you could see what it looks like. I hope this helps!
y-3 ≥ -12
Add 3 to both sides
y ≥ -9
What this means is that y could be any number as long as it’s greater than (bigger) or equal to -9, so y could equal -9, -3, 100, or 0 but could not equal -10,-11, -9.3, or anything less than -9
To graph this, first write in numbers below each of the lines. You want to show -9, a few numbers less than -9 and a few numbers greater than -9. It could look like this:
-11 -10 -9 -8 -7 -6 -5
Then, draw a filled in circle above -9. This shows that y can equal -9. Starting from where you drew the circle, draw an arrow to the right until the graph ends. This shows that y could be any of these numbers greater than -9, too.
I attached an example of a filled in number line for a different problem so you could see what it looks like. I hope this helps!
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The y-intercept of a function is that function's value when x=0.
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.
If you want them to differ by zero (be the same), you have to move them to the same point.
Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.
Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.
Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.
Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.
___
The appropriate choice is the 1st one.
f(x) - 3 and
g(x) + 1
.. f(0) = 4
.. g(0) = 0
These y-intercepts differ by 4.
If you want them to differ by zero (be the same), you have to move them to the same point.
Selection 1. Moves f(0) down 3 (to 1) and g(0) up 1 (to 1), so moves the y-intercepts to the same point. This is what you want, so this is an appropriate answer selection.
Selection 2. Moves f(0) up 4 (to 8) and g(0) down 1 (to -1). 8 and -1 are not the same point, so this is not the answer.
Selection 3. Moves f(0) down 2 (to 2) and g(0) up 1 (to 1). 2 and 1 are not the same point, so this is not the answer.
Selection 4. Moves f(0) up 3 (to 7) and g(0) down 6 (to -6). 7 and -6 are not the same point, so this is not the answer.
___
The appropriate choice is the 1st one.
f(x) - 3 and
g(x) + 1