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Section 1.5 – Analyzing Graphs of Functions

Section Details.
  • How to graph a function
  • Finding the domain and range of a function from the graph
  • Using the Vertical Line Test to determine if a graph represents a function
  • Zeros of a function and the \(x\) and \(y\)-intercepts
  • Determining the intervals where a function is increasing, decreasing, and constant
  • Finding relative maximums and relative minimums of a function
  • Definition of even and odd functions


Practice Problems


Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 
  1. ​Use the graph of the function \(f\) below to find \(f(-1)\), \(f(2)\), and \(f(4)\).

    \(f(-1)=3\)
    \(f(2)=DNE\)
    \(f(4)=DNE\)

    The domain of \(f\) is \([-3,2)\), so \(f(2)\) and \(f(4)\) are not defined.


    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V11

  2. Determine whether the function is even, odd, or neither. Then describe the symmetry.
    1. \(​f(x)=x\sqrt[3]{x^4+1}\)
    2. \(g(x)=\cfrac{x^4-9}{x^2+9}\)
    3. \(h(x)=x^3-3x^2\)

      1. Odd
      2. Even 
      3. Neither

      To see the full video page and find related videos, click the following link.
      WIR2 20B M150 V12

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