The graph at option 1 shows the given inequality y < x² + 1. The domain and range of the given inequality is {x: x ∈ (-∞, ∞)} and {y: y ∈ [1, ∞)}.
<h3>How to graph an inequality?</h3>
The steps to graph an inequality equation are:
- Solve for the variable y in the given equation
- Graph the boundary line for the inequality
- Shade the region that satisfies the inequality.
<h3>Calculation:</h3>
The given inequality is y < x² + 1
Finding points to graph the boundary line by taking y = x² + 1:
When x = -2,
y = (-2)² + 1 = 4 + 1 = 5
⇒ (-2, 5)
When x = -1,
y = (-1)² + 1 = 2
⇒ (-1, 2)
When x = 0,
y = (0)² + 1 = 1
⇒ (0, 1)
When x = 1,
y = (1)² + 1 = 2
⇒ (1, 2)
When x = 2,
y = (2)² + 1 = 5
⇒ (2, 5)
Plotting these points in the graph forms an upward-facing parabola.
So, all the points above the vertex of the parabola satisfy the given inequality. Thus, that part is shaded.
From this, the graph at option 1 is the required graph for the inequality y < x² + 1. The boundary line is dashed since the inequality symbol is " < ".
Learn more about graphing inequalities here:
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Answer:
slope = 2
Step-by-step explanation:
See the attachment for the markup.
It is usually convenient to choose places where the graph crosses grid intersections. Here, the graph crosses the x- and y-axes at integer values, so those points could be used, for example. We chose points away from the axes so that the rise and run lines could be seen more easily.
The graph has a rise/run of ...
slope = rise/run = 2/1 = 2
The slope of the line is 2.
Answer:
Step-by-step explanation:
Answer:
The one that does not belong has a different number of dimensions.
Step-by-step explanation:
<u>Given list consists of:</u>
- a line segment (AB)
- a plane (CDE)
- a line (FG)
- a ray (HI)
Three of them have one dimension but the plane has two dimensions,
therefore<u> </u>the plane in the list does not belong with the other three.
<u>So correct answer choice is:</u>
- The one that does not belong has a different number of dimensions.
