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3.1E: Functions and Function Notation (Exercises)

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    56069
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    For the following exercises, determine whether the relation is a function.

    1. \(\{(a, b),(c, d),(e, d)\}\)
    2. \{(5,2),(6,1),(6,2),(4,8)\}\)
    3. \(y^{2}+4=x,\) for \(x\) the independent variable and \(y\) the dependent variable
    4. Is the graph in Figure 1 a function?

    Graph of a parabola.

    For the following exercises, evaluate the function at the indicated values:

    \[\begin{array}{lllll} f(-3) ; & f(2) ; & f(-a) ; & -f(a) ; & f(a+h) .\end{array} \nonumber\]

    5. \(f(x)=-2 x^{2}+3 x\)
    6. \(f(x)=2|3 x-1|\)

    For the following exercises, determine whether the functions are one-to-one.

    7. \(f(x)=-3 x+5\)
    8. \(f(x)=\mid x-3\)

    For the following exercises, use the vertical line test to determine if the relation whose graph is provided is a function.

    9.

    Graph of a cubic function.

    10.

    Graph of a relation.

    11.

    Graph of a relation.

    For the following exercises, graph the functions.

    12. \(f(x)=\mid x+1\)
    13. \(f(x)=x^{2}-2\)

    For the following exercises, use Figure 2 to approximate the values.

    Graph of a parabola.

    14. \(f(2)\)
    15. \(f(-2)\)
    16. If \(f(x)=-2,\) then solve for \(x\).
    17. If \(f(x)=1,\) then solve for \(x\).

    For the following exercises, use the function \(h(t)=-16 t^{2}+80 t\) to find the values in simplest form.

    18. \(\frac{h(2)-h(1)}{2-1}\)
    19. \(\frac{h(a)-h(1)}{a-1}\)


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