2.3P: Practice

MTH 95: Algebra 3 · LibreTexts

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    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Progress

    Exercise

    Given the function defined by the rule

    \[ f(x) = \begin{cases} 0, & \text{if } x < 0 \\ 2, & \text{if } x \ge 0 \end{cases} \nonumber\]

    a. Draw the graph of \(f\) on a sheet of graph paper.
    b. Evaluate \(f(-2), f(0),\) and \(f(3)\) and plot these points on your graph.
    c. State the domain and range of \(f\).

    Exercise

    Given the function defined by the rule

    \[ f(x) = \begin{cases} -3, & \text{if } x < -2 \\ 1, & \text{if } -2 \le x < 2 \\ 3, & \text{if } x \ge 2 \end{cases} \nonumber\]

    a. Draw the graph of \(g\) on a sheet of graph paper.
    b. Evaluate \(g(-3), g(-2),\) and \(g(5)\) and plot these points on your graph.
    c. State the domain and range of \(g\).

    Exercise

    Determine a piecewise definition of the function described by the graph, then state the domain and range of the function.

    Graph image

    Exercise

    Given the piecewise function

    \[ g(x) = \begin{cases} 2x + 3, & \text{if } -2 \le x < 0 \\ -2x + 1, & \text{if } x \ge 0 \end{cases} \nonumber\]

    a. Draw the graph of \(g\) on a sheet of graph paper.
    b. Evaluate \(g(0)\) and \(g(3)\) and plot these points on your graph.
    c. State the domain and range of the function.

    Exercise

    Write a formula for the piecewise function graphed below:

    Graph of line segment from (-4,-3) to (1,2), line segment from (1,3) to (3,3), and line from (3,3) to (9,-10)

    Exercise

    A bakery has special deals on bulk orders of cookies. The first 100 cookies cost $2.00 each, the next 150 cookies cost $1.50 each, and any additional cookies beyond 250 cost $1.25 each.

    a. Sketch a graph of the cost of an order of cookies as a function of the number of cookies purchased. Clearly label the axes.
    b. Define variables and write a piecewise function to model this scenario.
    c. You may do parts a. and b. in either order - which do you find easier, graphing first or writing the function first?

     

    Exercise

    Jules left his house for a bike ride and rode straight to a coffee shop. He stayed at the shop for a while, then rode home. A graph of his ride is below.

    Graph of Jules' ride. Passes through the points (0,0), (1.5,18), (2,18), and (3.2,0)

    a. Define variables and write a piecewise function to model this scenario.
    b. State the domain and range of the function.

    Self-Check

    In this section, you practiced:

    1. Graphing piecewise functions given their formulas
    2. Writing a piecewise function given its graph
    3. Evaluating piecewise expressions

    From the list of skills above:

    1. I can complete these independently without notes:
    1. I can complete these, but need to reference an example or other resource to help:
    1. I don’t understand these yet:

    It’s okay to not be fully confident with every skill yet! But it’s essential to continue making progress. Identify at least one step you will take to improve your understanding of the topics you listed in parts 2 or 3 above:

    • Visit the math lab
    • Contact my instructor
    • Re-work practice problems
    • Ask a classmate or friend for help

    Which step(s) from above did you complete after last week's textbook practice?

    This page titled 2.3P: Practice was last modified on Wed, 10 Dec 2025 22:28:53 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.