The graph of the function f(x) = (x +2)(x + 6) is shown below. What is true about the domain and range of the function? The doma
2 answers:
1. The ''x-intercepts" of the graph of f(x) are those x-es such that
(x+2)(x+6)=0, so the x-intercepts or the roots are -2 and -6.
2. The axis of symmetry is the vertical line through the midpoint of -2 and -6, that is -4.
3. The vertex is the point (-4, f(-4))=(-4,(-4+2)(-4+6) )=(-4, (-2)(2))=(-4, -4)
4. The standard form of (x+2)(x+6) is
. The coefficient of 
is possitive so the parabola opens upwards.
5. This means the vertex (-4, -4) is the lowest point, so f(x) takes all values from -4 (inclusive) to + infinity. This determines the range
6. Any x can be "plugged in" f(x)=(x+2)(x+6) and be calculated, so x can be any number in R. This determines the domain to be all R.
7. Right choice is "<span>The domain is all real numbers, and the range is all real numbers greater than or equal to –4.</span>"
(x+2)(x+6)=0, so the x-intercepts or the roots are -2 and -6.
2. The axis of symmetry is the vertical line through the midpoint of -2 and -6, that is -4.
3. The vertex is the point (-4, f(-4))=(-4,(-4+2)(-4+6) )=(-4, (-2)(2))=(-4, -4)
4. The standard form of (x+2)(x+6) is
5. This means the vertex (-4, -4) is the lowest point, so f(x) takes all values from -4 (inclusive) to + infinity. This determines the range
6. Any x can be "plugged in" f(x)=(x+2)(x+6) and be calculated, so x can be any number in R. This determines the domain to be all R.
7. Right choice is "<span>The domain is all real numbers, and the range is all real numbers greater than or equal to –4.</span>"
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