>; < - dot line
≥; ≤ - solid line
>; ≥ - shading above the line
<; ≤ - shading below the line
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y = 2x + 3 - it's a linear function. We only need two points to plot the graph. Select two any x values and calculate the y values:
for x = 0 → y = 2(0) + 3 = 0 + 3 = 3 → (0, 3)
for x = -2 → y = 2(-2) + 3 = -4 + 3 = -1 → (-2, -1)
y > 2x + 3
Dot line an shading above the line (look at the picture).
I’m attaching a photo. For each of these, start by multiplying both sides of the inequality by what’s in the denominator.
When drawing of the number lines, the circle is filled in if the any quality has an “equal than.” Otherwise, the circle is left open.
When dividing by a negative number, the direction of the inequality flips. Greater than becomes less than, and vice-versa.
Use Socratic it always works usually but it’s faster
F(x) = x² + 2x - 1
f(2) = 2² + 2 · 2 - 1 = 4 + 4 - 1 = 7
f(-2) = (-2)² + 2 · (-2) - 1 = 4 - 4 - 1 = -1
f(3) = 3² + 2 · 3 - 1 = 9 + 6 - 1 = 14
f(-3) = (-3)² + 2 · (-3) - 1 = 9 - 6 - 1 = 2
The range = {-1; 2; 7; 14}
