Mathematics

Question

What are the domain and range of f(x) = 4* – 8?


domain: {x | x is a real number}; range: {yl y> -8}
domain: {x | x is a real number}; range: {yl y> 8}
domain: {x | x > 4}; range: {yly>-8}
domain: {x | x>-4}; range: {y | y>8}
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1 Answer

  • Answer:

    domain: {x | x is a real number}

    range: {y l y> -8}

    Step-by-step explanation:

    f(x) = 4x² – 8 is a parabola, a U shape.

    Since the stretch factor, 4, is positive, it opens up, there it will have a minimum value, the lowest point in the parabola.

    y > -8  because the minimum is -8.

    Parabolas do not have restricted "x" values. "4" does not restrict x because it is the stretch factor, which determines how wide the parabola is.

    Quadratic standard form:

    f(x) = ax² + bx + c

    "a" represents how wide the graph is. If it's negative it opens down, if it's positive it opens up.

    "b", if written, tells you it is not centred on the y-axis. It is not written, so the vertex is on the y-axis.

    "c" is the y-intercept. In this case, since b = 0, it is also the minimum value.

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