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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That would simplify to 32x^5+400x^4+200x^3+5000x^2+6250x+3125
You would do that because you have to write it repeatedly as (2x+5)(2x+5) and so on.
15-7 is 8! so 8 is the length of the side with the ?
Answer:
Step-by-step explanation:
factorise 216
since it is square root (meaning it has index to) pair up the number
Answer:
87: y = 5
88: y = 0
89: y = -2
90: y = -1/2x + 9
91: y = 2x - 16
92: y = x - 11
Step-by-step explanation:
To find the slope(m): (y1 - y2)/(x1 - x2)
To find the y-intercept:
y = mx + b
Replace m with the slope and x and y with one of the sets of coordinates. Then simplify to get the y-intercept. Use the equation y = mx + b and replace m with the slope and b with the y-intercept to get the equation.
(Sorry if this is a little confusing.)
