How do you graph the inequality #y>=-1#, #x>=3#?
See a solution process below:
First, we can graph the inequality
- A solid line at
#-1# on the vertical access, The line is solid because the inequality operator contains an "or equal to" clause. - Shade above the line because the inequality operation contains a "greater than" clause
graph{ y >= -1[-10, 10, -5, 5]}
First, we can graph the inequality
#x >= 3# as:- A solid line at
#3# on the horizontal access, The line is solid because the inequality operator contains an "or equal to" clause. - Shade to the right of the line because the inequality operation contains a "greater than" clause
graph{ x >= 3[-10, 10, -5, 5]}
Now, we can show where the two graphs intercept:
- A solid line at
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To graph the inequality ( y \geq -1 ) and ( x \geq 3 ), you would:
- Draw a solid horizontal line at ( y = -1 ) to represent ( y \geq -1 ).
- Shade the region above the line because it includes all points where ( y ) is greater than or equal to -1.
- Draw a solid vertical line at ( x = 3 ) to represent ( x \geq 3 ).
- Shade the region to the right of the line because it includes all points where ( x ) is greater than or equal to 3.
- The shaded regions where both conditions are satisfied (above the horizontal line and to the right of the vertical line) represent the solution set for the system of inequalities.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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