Question

Which graph shows y < x² +1? O 4) Intro •

Answer 1

What is inequality?

In Algebra, inequality shows the relation between two expressions using the inequality symbol.

The graph shows the equation y<x^2+1 is attached

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Answer 2

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, ∞)}.

How to graph an inequality?

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.

Calculation:

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 " < ".

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