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2.3E: Exercises

  • Page ID
    110609

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    Practice makes perfect!

    Determine values of a function using its graph

    Evaluate the following based on the graphs, then check your work by plugging the \(x\) value into the function to evaluate.

    1. \(f(x) = \sqrt{x + 4}\); \(f(-4), f(-3), f(0)\)

    graph_funct3.JPG

    1. \(f(x) = -3\); \(f(-3), f(0), f(4)\)

    graph_funct5.JPG

    3. \(f(x) = 2x + 1\); \(f(-2), f(0), f(2)\)

    graph_funct1.JPG

    Answer
    1. \(f(-4) = 0, f(-3) = 1, f(0) = 2\)
    2. \(f(-3) = -3, f(0) = -3, f(4) = -3\)
    3. \(f(-2) = -3, f(0) = 1, f(2) = 5\)
    Determine if a graph represents a function

    Use the vertical line test to determine if the following graphs represent a function:

    1. id_funct1.JPG
    2. id_funct3.JPG
    3. id_funct2.JPG
    4. id_funct4.JPG
    5. id_funct5.JPG
    Answer
    1. Not a function
    2. Function
    3. Not a function
    4. Function
    5. Function
    Determine domain and range of a function using a graph

    Determine the domain and range for each function represented by the graphs below:

    1. graph_funct1.JPG​​​​​​​
    2. graph_funct2.JPG​​​​​​​
    3. graph_funct3.JPG​​​​​​​
    4. graph_funct4.JPG​​​​​​​
    5. graph_funct5.JPG​​​​​​​
    6. graph_funct6.JPG​​​​​​​
    7. graph_funct7.JPG​​​​​​​
    8. graph_funct8.JPG​​​​​​​
    9. graph_funct9.JPG​​​​​​​
    10. graph_funct10.JPG
    Answer
    1. Domain: \((-\infty, \infty)\); Range: \((-\infty, \infty)\)
    2. Domain: \((-\infty, \infty)\); Range: \(y\geq 1\)
    3. Domain: \(x \geq -4\); Range: \(y\geq 0\)
    4. Domain: \((-\infty, \infty)\); Range: \(y\geq 5\)
    5. Domain: \((-\infty, \infty)\); Range: \(y = -3\)
    6. Domain: \((-\infty, \infty)\); Range: \((-\infty, \infty)\)
    7. Domain: \((-\infty, \infty)\); Range: \(y\geq 2\)
    8. Domain: \(x \geq -4\); Range: \(y\geq 2\)
    9. Domain: \((-\infty, \infty)\); Range: \(y\leq 3\)
    10. Domain: \((-\infty, \infty)\); Range: \(y = 3\)

    This page titled 2.3E: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Stanislav A. Trunov and Elizabeth J. Hale.

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