3.9.0: Review Exercises

Math 001: College Algebra · LibreTexts

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    Review Exercises

    Functions and Function Notation

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

    1.

    2.

    3.

    for the independent variable and the dependent variable

    4.

    Is the graph in Figure 1 a function?

    Graph of a parabola.
    Figure 1

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

    5.

    6.

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

    7.

    8.

    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.

    13.

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

    Graph of a parabola.
    Figure 2
    14.

    15.

    16.

    If then solve for

    17.

    If then solve for

    For the following exercises, use the function to find the values.

    18.

    19.

    Domain and Range

    For the following exercises, find the domain of each function, expressing answers using interval notation.

    20.

    21.

    22.

    23.

    Graph this piecewise function:

    Rates of Change and Behavior of Graphs

    For the following exercises, find the average rate of change of the functions from

    24.

    25.

    26.

    For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant.

    27.
    Graph of a parabola.
    28.
    Graph of a cubic function.
    29.
    Graph of a function.
    30.

    Find the local minimum of the function graphed in Exercise 1.27.

    31.

    Find the local extrema for the function graphed in Exercise 1.28.

    32.

    For the graph in Figure 3, the domain of the function is The range is Find the absolute minimum of the function on this interval.

    33.

    Find the absolute maximum of the function graphed in Figure 3.

    Graph of a cubic function.
    Figure 3
    Composition of Functions

    For the following exercises, find and for each pair of functions.

    34.

    35.

    36.

    37.

    38.

    For the following exercises, find and the domain for for each pair of functions.

    39.

    40.

    41.

    42.

    For the following exercises, express each function as a composition of two functions and where

    43.

    44.

    Transformation of Functions

    For the following exercises, sketch a graph of the given function.

    45.

    46.

    47.

    48.

    49.

    50.

    51.

    52.

    For the following exercises, sketch the graph of the function if the graph of the function is shown in Figure 4.

    Graph of f(x)
    Figure 4
    53.

    54.

    For the following exercises, write the equation for the standard function represented by each of the graphs below.

    55.
    Graph of an absolute function.
    56.
    Graph of a half circle.

    For the following exercises, determine whether each function below is even, odd, or neither.

    57.

    58.

    59.

    For the following exercises, analyze the graph and determine whether the graphed function is even, odd, or neither.

    60.
    Graph of a parabola.
    61.
    Graph of a parabola.
    62.
    Graph of a cubic function.
    Absolute Value Functions

    For the following exercises, write an equation for the transformation of

    63.
    Graph of f(x).
    64.
    Graph of f(x).
    65.
    Graph of f(x).

    For the following exercises, graph the absolute value function.

    66.

    67.

    68.

    For the following exercises, solve the absolute value equation.

    69.

    70.

    For the following exercises, solve the inequality and express the solution using interval notation.

    71.

    72.

    Inverse Functions

    For the following exercises, find for each function.

    73.

    74.

    For the following exercise, find a domain on which the function is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of restricted to that domain.

    75.

    76.

    Given and

    1. Find and
    2. What does the answer tell us about the relationship between and

    For the following exercises, use a graphing utility to determine whether each function is one-to-one.

    77.

    78.

    79.

    If find

    80.

    If find

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